Using mathematical induction I want to show that $\displaystyle 3^{6n}-2^{6n}$ is divisible by $\displaystyle 35$, $\displaystyle \forall n \in \mathbb{N}$.

The base case n=1 is true: $\displaystyle 3^6-2^6=665$, 665/35=19.

Inductive step: Suppose $\displaystyle 3^{6k}-2^{6k}$ is divisible by 35 for some $\displaystyle k \in \mathbb{N}$. That means $\displaystyle 3^{6k}-2^{6k} = 35m$ for some m. Then

$\displaystyle 3^{6(k+1)}-2^{6(k+1)}= 3^{6k}.3^6-2^{6k}.2^6$

Now how can I simplify this to factor out $\displaystyle 3^{6k}-2^{6k}$ to show that it's divisible by 35 for k+1?