Prove that n^3-n is divisible by three through mathematical induction where n is a positive interger

Question

Prove through mathematical induction

Answer 1

For n=1, we have 1-1=0, 0 is divisible by 3.

Assume that this is true for n and we have to show that its true for n+1 

(n+1)³-(n+1)=n³+3n²+2n=n³-n+3(n²+n) is divisible by 3; n³-n by 3 by is divisible by assumption and 3(n²+n) is divisible as well. So, if  n3-n is divisible by 3, then (n+1)³-(n+1) is divisible as well.