7. The set of all natural numbers $n$ that make $3^{2 n+1}-2^{2 n+1}-6^{n}$ a composite number is
7. $N^{4} \backslash \mid 1=$
$$
3^{2 n+1}-2^{2 n+1}-6^{n}=\left(3^{n+1}+2^{n+1}\right)\left(3^{n}-2^{n}\right)
$$

Since $3^{n+1}+2^{n+1}>1$, the above expression is composite only if $3^{n}-2^{n}>1$, i.e., $n>2$.