# Cubing

A number whose cube root is an integer is called a perfect cube.

# Properties of a Cube

- The sum of the cubes of any number of consecutive integers starting with 1 is the square of some integer.
^{3 }+ 2^{3 }= 9 = 3^{2}, 1^{3 }+ 2^{3 }+ 3^{3 }= 36 = 6^{2}, etc.) - Unit digit of any cube can be any digit from 0-9.

# Methods of Cubing

We can find the cube of any number close to a power of 10 say 10

^{n}with base = 10^{n}by finding the surplus or the defict (*x*). The answer will be obtained in three parts.B + 3

*x*| 3 .*x*^{2}|*x*^{3}^{}The left two parts will have n digits.104

^{3}^{}Base B = 100 and surplus =*x*= 4(100 + 3 Ã— 4)|3 Ã— 4

^{2}|4^{3}= 112|48|64 = 1124864109

^{3}^{}Base B = 100 and*x*= 9(100 + 3 Ã— 9)|3 Ã— 9

^{2}|9^{3}= 127|243|729 = 129502998

^{3}^{}Base B = 100 and*x*= âˆ’2(100 âˆ’ 3 Ã— 2) | 3 Ã— (âˆ’2)

^{2}| (âˆ’2)^{3}= 94 | 12 | âˆ’8 = 94 | 11 | 100 â€“ 8 = 941192