We have to look at the numbers from 1 to 9. Cube of 1 (1 3 ) = 1 Cube of 2 (2 3 ) = 8 Cube of 3 (3 3 ) = 27 Cube of 4 (4 3 ) = 64 Cube of 5 (5 3 ) = 125 Cube of 6 (6 3 ) = 216 Cube of 7 (7 3 ) = 343 Cube of 8 (8 3 ) = 512 Cube of 9 (9 3 ) = 729 Cube of 10 (10 3 )=1000 Some important things:- 1. The sum of the digits of a perfect cube number can only be 1, 8 and 9, so if the sum of the digits is any other than these three, then that number cannot be a perfect cube. 2. The numbers to the right of which zeros are not multiples of three are incomplete cube numbers like 100, 10000, 2160000 etc. 3. As many groups of 3–3 digits are formed in a perfect cube number, there will be as ma...