Sum it up to 1729

Algebra Level 4

If \(V_{n}=a^{n}+b^{n},\) where \(a\) and \(b\) are the roots of \(x^{2}+x+1,\) what is the value of \[ \sum_{n=0}^{1729} (-1)^{n} \cdot \ V_{n} ?\]

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