n is an odd integer. Which of these expressions is always odd?

For odd $n$, both $n^2$ and $n^3$ are odd. So $n^2+2n$ = odd + even = odd, which is the answer. The others are all even: $n^2+n$ = odd + odd, $3n+1=$ odd + 1, and $n^3-n$ = odd − odd.