Algebra or Number Theory?

Number Theory Level 3

$\big(n^2 + 2n + 2\big) \, \Big| \, \big(n^3 + 4n^2 + 4n - 14\big)$ Find the sum of all integers $n$ such that the above holds true.

Notation: $a \mid b$ means $a$ is a factor of $b$ .