How to find cube root by successive subtraction method and how to take out the numbers by which number has to be subtracted?

Method of successive subtraction to find the cube root:

1) We Subtract the numbers 1, 7 ,19 ,37, 61, 91,… successively from the given number untill we get zero.

2) The count of subtractions will give the cube root of the number.

3) The n^th term of sequence 1, 7, 19, 37, 61, 91,… is

a_n = 1 + 3n(n – 1)

Example:

Take 64

64 – 1 = 63

63 – 7 = 56

56 – 19 = 37

37 – 37 = 4

As, subtraction is done four times, cube root of 64 is 4.