Is the language $a^nwa^n$ regular?
Your language is regular, since it is identical to $a\Sigma^*a$.

Indeed, by definition of $L$, every word of the form $a\Sigma^*a$ is in $L$ (take $n = 1$). Conversely, every word in $L$ starts and ends with $a$ (and is of length at least 2), and so is of the form $a\Sigma^*a$.