Perfect Cube Formula

Perfect Cube Formula

The perfect cube formula helps in representing any number in the form of its cube root. Whenever any number is multiplied three times, then the resultant answer is known as the cube of that number. Thus, the cube for the number (a) becomes a3 or a-cubed. A perfect cube is defined as the number whose cube root is an integer value. 

What is the Perfect Cube Formula?

The perfect cube formula is used to check if any number is a perfect cube or not. Suppose we have a number, x, such that, x = y × y × y. Perfect cube formula of any number(x) can be expressed as:

x = y3


y =∛x


  • x = perfect cube
  • y = cube root of x

Here, cube root of x, y will have an integral value. Let us have a look at a few examples on the perfect cube formula to understand the concept better.

Solved Examples Using Perfect Cube Formula

Example 1: Using the perfect cube formula, calculate the cube root of 216.


To find: Cube root of 216


216 = 2 × 2 × 2 × 3 × 3 × 3

216 = (2 × 3)3

Using the perfect cube formula,  

216 = (2 × 3)3

Thus, Cube root of 216 = 6

Answer: Cube root of 216 = 6

Example 2: Using the perfect cube formula, check if 343 is a perfect cube.


To find:

Whether 343 is a perfect cube

From Prime Factorization of 343, we get,

 343 = 7 × 7 × 7 

216 = 73

Using the perfect cube formula,

Cube root of 343 = 7

which is an integral value.                                                                                                          

Answer:  343 is a perfect cube.