For induction, there are 2 steps.
1. Show that some concrete value satisfies your relation.
2. Suppose the relation is true for n, and then show it is true for n+1.
For your case, you can show that
6 | 1^3 - 1.
Then assume that
6 | n^3-n for some n , and show that
6 | (n+1)^3-(n+1), where this n is the same n in the previous line.
Expand the cubic term, note that the terms remaining after the subtraction are 3(n)(n+1) and show that
6 | 3(n)(n+1)