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Cubing

A number whose cube root is an integer is called a perfect cube.
Description: vm-23.tif

Properties of a Cube

  1. The sum of the cubes of any number of consecutive integers starting with 1 is the square of some integer.
     
    (For example, 13 + 23 = 9 = 32, 13 + 23 + 33 = 36 = 62, etc.)
  2. 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 10n with base = 10n by finding the surplus or the defict (x). The answer will be obtained in three parts. 
B + 3x | 3 . x2 | x3
 
The left two parts will have n digits.
1043
 
Base B = 100 and surplus = x = 4
(100 + 3 × 4)|3 × 42|43 = 112|48|64 = 1124864
1093
 
Base B = 100 and x = 9
(100 + 3 × 9)|3 × 92 |93 = 127|243|729 = 1295029
983
 
Base B = 100 and x = 2
(100  3 × 2) | 3 × (2)2 | (2)3 = 94 | 12 | 8 = 94 | 11 | 100 – 8 = 941192




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