Perfect Cube Calculator

Created by Madhu Raman
Reviewed by Wojciech Sas, PhD candidate and Steven Wooding
Last updated: Apr 13, 2022

Are you searching for a quick tool that helps you identify if a number is a perfect cube? Look no further! Our perfect cube calculator will tell you if we can write a given number as the cube of an integer or not! Read on to know what a perfect cube is, how to find a perfect cube, and a list of some perfect cubes!

A cube is generally any number obtained by raising a given number to the power of 3. An interesting application of this concept lies in finding the volume of a cube.

Perfect cube definition

A perfect cube number is the number that results by raising an integer to the power of 3.

In other words, if we multiply an integer by itself three times, we get a perfect cube!

So mathematically, the following is the perfect cube formula:

A number N is a perfect cube if we can write it as:

N = a * a * a,

where a is an integer.

Generally, if we can find what the cube root of a number is, and if that is an integer, our number will be a perfect cube!

How do we use the perfect cube calculator?

If you want to find out if a number N is a perfect cube or not, simply key in its value into the Number field of the calculator!

The perfect cube calculator will then tell you if the number is a perfect cube, and if yes, you will also be able to see its cube root!

Which numbers are perfect cubes?

Here are some examples of perfect cubes:

  • 2Β³ = 2 * 2 * 2 = 8, so 8 is a perfect cube!

  • Similarly, (-2)Β³ = (-2) * (-2) * (-2) = -8, so -8 is also a perfect cube!

  • 6Β³ = 6 * 6 * 6 = 216, so 216 is a perfect cube!

  • Similarly, (-6)Β³ = (-6) * (-6) * (-6) = -216, so -216 is also a perfect cube!

Unlike square root, we can find cube roots for negative numbers too!

Some other examples of identifying perfect cubes are:

  • Given the number 100, its cube root is approximately 4.64, which is not an integer. So 100 is not a perfect cube.

  • Given the number -1000, its cube root is -10, which is an integer. So -1000 is a perfect cube number, which you can also check by using our perfect cube calculator!

  • Given the number 125,000, its cube root is 50, which is an integer. So, 125,000 is a perfect cube number which you can also verify, using our perfect cube calculator!

List of Perfect Cubes

Here's a list of the first 10 perfect cubes for ready-reference:

Number | Cube of number
1 | 1
2 | 8
3 | 27
4 | 64
5 | 125
6 | 216
7 | 343
8 | 512
9 | 729
10 | 1000

Similar to perfect cubes, we also have perfect squares, which are numbers whose square roots will be integers.

A few interesting extensions of the concept of roots in general are:

Hey! We thought that instead of perfect cubes you may be looking for magic squares: go to our magic square calculator and learn everything about them!

FAQ

Can the cube root of a number be negative?

Yes! The cube root of any negative number will always be negative, and the cube root of any positive number will always be positive.

Is 125 a perfect cube?

Yes! We can write 125 as 5 Γ— 5 Γ— 5, which means that the cube root of 125 is 5.

Since 5 is an integer, 125 is a perfect cube πŸŽ‰!

Is 64 a perfect cube?

Yes! We can write 64 as 4 Γ— 4 Γ— 4, which means that the cube root of 64 is 4.

Since 4 is an integer, 64 is a perfect cube πŸŽ‰!

Is 27 a perfect cube?

Yes! We can write 27 as 3 Γ— 3 Γ— 3, which means that the cube root of 27 is 3.

Since 3 is an integer, 27 is a perfect cube πŸŽ‰!

Is 8 a perfect cube?

Yes! We can write 8 as 2 Γ— 2 Γ— 2, which means that the cube root of 8 is 2.

Since 2 is an integer, 8 is a perfect cube πŸŽ‰!

Is 1 a perfect cube?

Yes! We can write 1 as 1 Γ— 1 Γ— 1, which means that the cube root of 1 is 1 itself.

So 1 is a perfect cube πŸŽ‰!

Is 0 a perfect cube?

Yes! We can write 0 as 0 Γ— 0 Γ— 0, which means that the cube root of 0 is 0 itself.

So 0 is a perfect cube πŸŽ‰!

Madhu Raman
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