Ok so our hypothesis is that

So lets begin

Base Step:

When we have

So that is true

Restate the hypothesis:

Inductive step: Now we have to just using the hypothesis prove that

Now rexpanding this we get

Rewriting this we get

Now by our hypothesis the first term is divisible by six, so it follows that we must just prove that

Now if is odd then is even so

So there is a factor of two in so there is a factor of six in and consequently in

Now if is even then is even and the same argument follows.

So we have proved our iductive step and the result follows.

EDIT: Moo has informed me that I have the notation backwards, for my sake just pretend that means that the left hand side is divides the right hand site.