Proving by induction that $(5^{2n})-1$ is divisible by $8$ and $3$

Question

Prove by induction that for all integers n that $5^{2n}-1$ is divisible by $8$ and $3$. Explain

Answer 1

$5^{2(n+1)}-1=25\times5^{2n}-1=25\times5^{2n}-25+24=25\times(5^{2n}-1)+24$

And so we can see that if $5^{2n}-1$ is divisible by 3 and 8, then $5^{2(n+1)}-1$ is ... ?