Proof that an expression is divisible by a certain integer (power type)

Prove the following:

3^{2n} – 1 is divisible by 8
or 3^{2n} – 1 is a multiple of 8

The method of induction:

Start by proving that it is true for n=1, then assume true for n=k and prove that it is true for n=k+1. If so it must be true for all positive integer values of n.

Proof that an expression is divisible by a certain integer (non-power type)