1. 152 For which natural numbers $n$ is the number $3^{2 n+1}-2^{2 n+1}-6^{n}$ composite.
[Solution] Since $3^{2 n+1}-2^{2 n+1}-6^{n}=\left(3^{n}-2^{n}\right)\left(3^{n+1}+2^{n+1}\right)$, and when $n>1$, we have $3^{n}-2^{n}>1$, so when $n>1$, the original number is composite; on the other hand, when $n=1$, the number equals 13, which is a prime number. Therefore, the solution to this problem is $n>1$.