Algebra or Number Theory?

(n2+2n+2)(n3+4n2+4n14) \big(n^2 + 2n + 2\big) \, \Big| \, \big(n^3 + 4n^2 + 4n - 14\big) Find the sum of all integers nn such that the above holds true.


Notation: aba \mid b means aa is a factor of bb.

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