# How to obtain the cube of a number ?

It is often difficult to obtain the cube a number, simply because because there is too much computation involved. We have already discussed a  Mathematical Shortcut : How to obtain the cube of a number where we modify the existing formula to obtain the cube of that number.

However, that technique proposed in Mathematical Shortcut : How to obtain the cube of a number assumes that we should know the cubes of certain numbers. However, for certain numbers, we might not know know the cubes. In such cases, the can use this technique.

You can practice, whichever technique, you feel is easier.

Consider a general example. Let’s say we want to obtain the cube of the number a. We can write it as,

a3 = (a-d) * a * (a+d) + ad2

Step 1 : Obtain the product of the integers (a-d), a, (a+d)

Step 2 : Add ad2 to the product obtained in Step 1. The result obtained will be equal to a3

Notice that when d=1, the numbers are consecutive integers a-1, a, a+1. And you add a to the product.

Consider a very simple example. Let’s say we want to obtain the cube of 11.

The entire steps are illustrated in the following figure.

Step 1 : Obtain the product 10 x11x12 (multiple of consecutive Integers) to get 1320.

Step 2 : Add 11 to this product. We get 1320+11=1331. So, 113=1331.

Consider another example: Say we want to obtain the cube of 25.

Step 1 : Obtain the product 24x25x26 (multiple of Consecutive Integers). Instead of multiplying 3 numbers, we can simplify this by converting 25 to 100/4. So we get,

24×25×26= (24×100×26)/4

Step 2 : Add 25 to this product. We get 15600+25=15625.

Very easy Right 🙂 ? So far we considered numbers where d=1. However, this does not have to be the case all the time.

Consider another example: Let us we want to obtain the cube of 28.

So 283 = (28 – 2) x 28 x (28 + 2) + 28×22

Step 1 : Obtain the product 26x28x30 = 21840.

Step 2 : Add 28×22=112. We get 21840+112=21952.

Very easy right 🙂

Note : This technique is very useful when the number is closer to a number having a unit digit of 5 or 0. For example, 14, 16, 19, 21, 31 etc.

Exercise:  Using this technique, obtain the cubes of the following:

• 19
• 21
• 31
• 34

I have presented both the shortcuts here and here.  Practice the technique, you feel more comfortable in.