elementary number theory - Prove by induction that $3^n +7^n −2$ is divisible by $8$ for all positive integers $n$...

Prove by induction that $3^n +7^n −2$ is divisible by $8$ for all positive integers $n$.

So far I have the base case completed, and believe I am close to completing the proof itself.

Base case:$(n=1)$

$3^1 + 7^1 - 2 = 8/8 = 1 $

Inductive Hypothesis: Assume that $3^n +7^n −2$ is divisible by 8 for all positive integers n.

Induction step $(n+1)$ case:

$$ 3^{n+1} + 7^{n+1} - 2 $$

$$3(3^{n}) + 7(7^{n}) - 2$$

$$3^n + 7^n = 8x $$

-It seems to me that this could be the end of the proof because whatever the answer is would be a multiple of 8: but I am unsure, any help is appreciated.