# Perfect Cube Calculator

URL: https://speedycalculator.com/calculators/math/perfect-cube/
Last updated: 2026-10-30

> The perfect cube calculator checks whether an integer is a perfect cube (the cube of a whole number), gives its cube root and the nearest cubes on either side.

## Inputs

- Number

## Results

- Result
- Cube root
- Nearest perfect cubes
- Prime factorisation

## Formula

```
N is a perfect cube ⇔ N = a³ for some integer a ⇔ every prime exponent is a multiple of 3
```

## Explanation

Perfect cubes – 1, 8, 27, 64, 125 … – are the volumes of cubes with whole-number sides. Recognising them helps with simplifying cube roots and factoring sums and differences of cubes.

### How to use the Perfect Cube Calculator

- **Number**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The integer cube root is computed exactly and cubed again to test. The prime factorisation is shown too: in a perfect cube every exponent is divisible by 3.

## Worked example

Inputs — Number: 125.

Results — **Result = 125 is a perfect cube: 5³ = 125**; Cube root = 5; Prime factorisation = 5³.

## Key terms

- **Perfect cube**: The cube of an integer.

## FAQ

**Is 1,000 a perfect cube?**
Yes: 10³.

**Can a negative number be a perfect cube?**
Yes: −27 = (−3)³.

**How do I recognise a perfect cube from its prime factors?**
Every exponent is a multiple of 3, e.g. 216 = 2³ × 3³.

**What are the first ten cubes?**
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.


## Sources

- [OpenStax – Contemporary Mathematics](https://openstax.org/details/books/contemporary-mathematics)
- [Wolfram MathWorld – Prime factorization](https://mathworld.wolfram.com/PrimeFactorization.html)