This is a rather easy exercise - using either induction or direct proof (unless I am missing something in the question)
I have a back-door approach to this one . . .
As aman-cc pointed out: .
I recognized this is as part of the formula for the sum of consecutive squares:
Since the left side is an integer, the right side must be an integer.
. . That is, is a multiple of 6.
Therefore: . .for all integer values of