Algebra or Number Theory?

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


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

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