Volume of a Cube: Formula, Examples, and How to Find It

The volume of a cube is the amount of three-dimensional space inside the cube. Because all six faces of a cube are equal squares, all of its edges have the same length. This makes the volume of a cube easy to calculate: multiply the side length by itself three times, or use the formula V = s³.

In this guide, you will learn how to find the volume of a cube, understand why the formula works, solve volume problems step by step, and avoid common mistakes with cubic units. You will also see how to find the side length when the volume is given.

What Is the Volume of a Cube?

The volume of a cube measures how much space a cube occupies. It can also be understood as the number of unit cubes needed to fill the cube completely.

A cube is a three-dimensional shape with:

• 6 square faces
• 12 equal edges
• 8 vertices
• Equal length, width, and height

For example, imagine a cube with an edge length of 4 inches. You could fill it with small unit cubes. There would be:

4 × 4 × 4 = 64

unit cubes.

Therefore, the cube has a volume of 64 cubic inches.

This idea leads directly to the volume formula. A cube can be viewed as a special rectangular prism in which the length, width, and height are all equal.

The general volume formula for a rectangular prism is length × width × height. When all three measurements are the same, the formula becomes s × s × s.

Volume of a Cube Formula

The standard volume of a cube formula is:

V = s³

Where:

• V = volume of the cube
• s = length of one edge
• s³ = s × s × s

The exponent 3 means that you multiply the side length three times.

For example:

s = 5 cm

V = 5³

V = 5 × 5 × 5 = 125 cm³

So, the volume is 125 cubic centimeters.

Volume vs. Surface Area of a Cube

Volume and surface area describe different properties of a cube. Volume measures the space inside the cube, while surface area measures the total area of its outside faces.

A useful way to remember the difference is:

Area uses square units. Volume uses cubic units.

For example, if the side length is measured in centimeters, the volume is measured in cm³, not cm².

How to Find the Volume of a Cube

Finding the volume of a cube only requires one measurement: the length of one edge. Since every edge of a cube has the same length, you do not need separate measurements for length, width, and height.

Follow these three steps.

Step 1: Find the Side Length

Look at the cube and identify the length of one edge.

For example:

s = 6 cm

You only need one side because every edge of the cube is equal.

Step 2: Use the Volume of a Cube Formula

Write the formula:

V = s³

Then substitute the side length:

V = 6³

You can also write it as:

V = 6 × 6 × 6

Step 3: Calculate and Add Cubic Units

Calculate:

6 × 6 × 6 = 216

Because the original measurement was in centimeters, the volume is:

V = 216 cm³

Therefore, a cube with a side length of 6 cm has a volume of 216 cubic centimeters.

Quick Formula Guide

Volume of a Cube: Worked Examples

Understanding how to find the volume of a cube becomes easier when you work through different types of problems.

Example 1: Side Length Is Given

Problem: Find the volume of a cube with a side length of 7 inches.

Solution:

Use the formula:

V = s³

Substitute 7 for s:

V = 7³

Multiply:

V = 7 × 7 × 7

V = 343

Because the measurement is in inches, the volume is:

Answer: 343 in³

The volume of the cube is 343 cubic inches. The same step-by-step approach is commonly used in elementary and middle-school volume problems.

Example 2: A Real-World Cube

Problem: A cube-shaped storage box has an edge length of 10 inches. How much space is inside the box?

The box is a cube, so use:

V = s³

Substitute:

V = 10³

Calculate:

V = 10 × 10 × 10 = 1,000

Therefore:

Answer: 1,000 in³

The box can hold 1,000 cubic inches of space.

Example 3: Finding the Side Length From Volume

Sometimes the volume is given, but the side length is unknown.

Problem: A cube has a volume of 512 cm³. What is the length of one edge?

Start with:

V = s³

Substitute the volume:

512 = s³

Now take the cube root of both sides:

s = ∛512

Because:

8 × 8 × 8 = 512

we get:

s = 8 cm

Answer: 8 cm

So, when you know the volume of a cube and need to find its side length, use the cube root.

Example 4: Different Units

Suppose a cube has a side length of 0.5 meters.

Use:

V = s³

V = 0.5³

V = 0.5 × 0.5 × 0.5

V = 0.125 m³

The answer is:

0.125 cubic meters

Always make sure the side length is expressed in the unit you want to use before calculating the volume. The resulting unit must also be cubed.

Common Mistakes When Finding the Volume of a Cube

The formula itself is simple, but students often make mistakes when applying it.

1. Multiplying the Side by 2 Instead of 3 Times

A common error is:

V = s × 2

This does not calculate volume.

The correct formula is:

V = s × s × s = s³

For a cube with a side length of 4:

4 × 4 × 4 = 64

not 8.

2. Using Square Units Instead of Cubic Units

Volume is three-dimensional, so the final unit must be cubic.

Correct:

125 cm³

Incorrect:

125 cm²

Remember:

• Length → units
• Area → square units
• Volume → cubic units

3. Confusing Volume With Surface Area

The volume formula is:

V = s³

The surface area formula is:

SA = 6s²

If a question asks how much space is inside a cube, you need volume. If it asks how much material is needed to cover the outside, you need surface area.

4. Forgetting to Cube Decimal Numbers

Decimals must also be multiplied three times.

For example:

V = 0.2³

= 0.2 × 0.2 × 0.2

= 0.008

Therefore, the volume is 0.008 cubic units.

Practice Problems: Volume of a Cube

Once students understand the formula, practice helps them recognize which information matters and calculate more accurately. Volume worksheets commonly include problems where students are given a side length, solve word problems, or work backward from a given volume.

Try these problems:

For each problem, start by identifying what is given. If the side length is known, use V = s³. If the volume is known and the side length is missing, use the cube root.

FAQ

1. What is the formula for the volume of a cube?

The formula is V = s³, where s represents the length of one edge. Because all edges of a cube are equal, you multiply the side length by itself three times.

2. How do you find the volume of a cube?

To find the volume of a cube, first find the length of one edge. Then use V = s³, or multiply the side length × side length × side length. Finally, write the answer in cubic units.

3. What is the volume of a cube with a side of 5?

Use:

V = 5³ = 5 × 5 × 5 = 125

Therefore, the volume is 125 cubic units. If the side is 5 cm, the answer is 125 cm³.

4. How do you find the side length of a cube when you know its volume?

Take the cube root of the volume:

s = ∛V

For example, if the volume is 216 cm³:

s = ∛216 = 6 cm

5. What units are used for the volume of a cube?

Volume is measured in cubic units, such as:

• cubic inches (in³)
• cubic feet (ft³)
• cubic centimeters (cm³)
• cubic meters (m³)

The unit is cubed because volume measures three dimensions: length, width, and height.

Conclusion

The volume of a cube tells you how much three-dimensional space the cube contains. Since every edge of a cube has the same length, you only need one measurement to calculate its volume. The key formula is V = s³, which means multiplying the side length by itself three times.

To find the volume of a cube, identify the edge length, substitute it into the formula, calculate the result, and express the answer in cubic units. When the volume is given instead, use the cube root to find the missing side length.

For students who want more structured support with math concepts and problem-solving, WuKong Education’s math courses can provide guided practice and instruction suited to different learning levels.

Nathan | WuKong Math Teacher

Nathan, a graduate of the University of New South Wales, brings over 9 years of expertise in teaching Mathematics and Science across primary and secondary levels. Known for his rigorous yet steady instructional style, Nathan has earned high acclaim from students in grades 1-12. He is widely recognized for his unique ability to blend academic rigor with engaging, interactive lessons, making complex concepts accessible and fun for every student. Nathan also has extensive experience helping students prepare for the AMC 8 and Math Kangaroo competitions, guiding them to achieve outstanding results in international math contests.