Complexity! (7)

Algebra Level 4

Evaluate the following sum in terms of $n$ ,

$\displaystyle \sum_{k=1}^n (k+1)\left(k + \dfrac{1}{\omega}\right)\left(k + \dfrac{1}{\omega^2}\right)$

Notations: $\omega$ and $\omega^2$ are non-real cube roots of unity.

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