Question

Find the smallest number that must be subtracted from 682 to make it a perfect cube

Answer 1

Perfect cube is the cube of an integer 
ie x*x*x while x is an integer 
so perfect cubes near 682 are 8 cube which is 8x8x8 = 512
9 cube = 9x9x9 = 729
since the least number was supposed to be subtracted from the given number 
let the unknown least be x 
682 - x = 512
682 - 512 = x
170 = x
the least number to be subtracted to make it a perfect cube is 170

Answer 2

In order to make it as perfect cube, once should know the cubes till 10
Number : Cube
1 : 1
2 : 8
3 : 27
4 : 64
5 : 125
6 : 216
7 : 343
8 : 512
9 : 729

Hence in 8 becomes the perfect cube which is close to 682. Hence 170 should be deducted from 692 to make it as perfect cube