We have :  \( { (a+b) }^{ 3 } \) = \( { a }^{ 3 } \) + 3 \( { a }^{ 2 } \) b+ 3 a \( { b }^{ 2 } \) + \( { b }^{ 3 } \).
Method : For finding the cube of a two-digit number with the tens digit = a and the units digit b, we make four columns, headed by
        \( { a }^{ 3 } \), 3 \( { a }^{ 2 } \) b, 3 a \( { b }^{ 2 } \) and \( { b }^{ 3 } \).
The rest of the procedure is the same as followed in squaring a number by the column method.

We simplify the working as :

Short-Cut-Method-For-Finding-The-Cube-Of-A-Two-Digit-Number

Example 1: Find the value of \( { (29) }^{ 3 } \) by the short-cut method.
Solution. Here,            a=2 and b=9

Short-Cut-Method-For-Finding-The-Cube-Of-A-Two-Digit-Number-example-1            

                 Therefore,        \( { (29) }^{ 3 } \) = 24389.

Example 2: Find the value of \( { (71) }^{ 3 } \) by the short-cut method.
Solution. Here, a = 7 and b = 1.

Short-Cut-Method-For-Finding-The-Cube-Of-A-Two-Digit-Number-example-2

                   Therefore,     \( { (71) }^{ 3 } \) = 357911.