Where EXACTLY are you stuck? Have you already checked for n = 1? Then, what is your inductive asusmption (hypothesis)?

It's possible to do it without induction, too:

(1) if n is an odd multiple of 3 then n^2 is odd and thus n^2 + 5 is even ==> the product n(n^2 + 5) is divisible both by 2 and 3 and thus by 6

(2) if n is an even multiple of 3 then it is a multiple of 6...

(3) if n is NOT a multiple of n the n^2 + 5 is ALWAYS a multiple of 3 (right n = 1 or 2 + 3k,. with k an integer, and square this and add to 5): if n is odd then n^2 + 5 is even, and if n is even good: in any case, the product n(n^2 + 5) is divisible both by 2 and by 3.

Tonio