Mathematical induction proof

Hello everybody,
I am doing my reading lately to prepare for some exams to join a mathematics department.

And I would very much like, if anyone could help, the solution (or a hint) to the following induction proof.

" Show that n^3 + (n+1)^3 + (n+2)^3 is a multiple of 9 "



I can deal with proofs that say " *this* is divisible with *that* " but in that case I have no clue how to start.

I have noone to ask for help ... but you in the forum.

 

Thanks for the answer,

Okay, here is my solution. I thought that at the problem defintion "is divisible by" and "is a multiple of" makes a huge difference.

The base case is obvious.

Let that the statement holds for n=k, that is,
[tex]k^3+(k+1)^3+(k+2)^3[/tex] is a multiple of 9.
We will then show that it holds for n=k+1, that is [tex](k+1)^3+(k+2)^3+(k+3)^3[/tex] is a multiple of 9.

We have,
[tex]k^3+(k+1)^3+(k+2)^3+(k+3)^3-k^3=9M+(k+3)^3-k^3[/tex],
So what we want to show is that [tex](k+3)^3-k^3[/tex] is also a multiple of 9.
By using the formula [tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex] we can reach our goal.