# Cube Formula

Cube of any digit, forms by multiplying the digit by itself three times. For instance, to find the cube of 5, i.e. 53we need to multiply 5 three times: 5 × 5 × 5 = 125

Note: We can write “5 cube” as

$$\begin{array}{l}5^{3}\end{array}$$
. Here, the number 3 on the exponent’s place means the number appears three times during the multiplication process.

The Cube Formula for any value ‘x’ is given as,

$\LARGE x^{3} = x \times x \times x$
In algebra, cube refers to a number raised to the power 3. However, the meaning of cube is different in geometry, i.e. cube is a 3d shape with equal measure of edges and all the faces are squares.
Based on this, we can also write the volume of cube formula since cube has equal length, breadth and height.
Length = Breadth = Height = a
Thus, the measure of each edge of the cube = a
Therefore, the volume of cube formula is a × a × a = a3.
It is to be noted that the number obtained using cube formula is the perfect cube number.

### Solved Examples

Question 1:
What is the cube of 15?
Solution:
The formula for calculating cube is,
$$\begin{array}{l}x^{3} = x \times x \times x\end{array}$$
Here, x = 15
$$\begin{array}{l}15^{3} = 15 \times 15 \times 15\end{array}$$
Therefore,
$$\begin{array}{l}15^{3} = 3375\end{array}$$
Question 2:
What is the value of x if
$$\begin{array}{l}x^{3}=27\end{array}$$
?
Solution:

The formula for calculating cube is,
$$\begin{array}{l}x^{3} = x \times x \times x\end{array}$$
Here,
$$\begin{array}{l}x^{3}=27\end{array}$$
$$\begin{array}{l}x=\sqrt[3]{27}\end{array}$$
Therefore,
$$\begin{array}{l}x = 3\end{array}$$
 More topics in Cube Formula Volume of Cube Formula Difference of Cubes Formula