For $\mathrm{n}\in \mathrm{N},3^{2\mathrm{n}+2}-2^3\mathrm{n}-9$ is divisible by

For n=1, we have

$3^{2\mathrm{n}+2}-2^3\mathrm{n}-9=81-8-9=64$ ,which is divisible by 64

For n = 2, we have

$\begin{array}{rl} & 3^{2\mathrm{n}+2}-2^3\mathrm{n}-9\\ & =3^6-2^3\times 2-9\\ & =729-16-9\end{array}$

= 704, which is divisible by 64.