So lets begin
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.