Newton's Sums, here?

Algebra Level 5

$\large x^3 + 2x^2 - 3x - 1 = 0$

If $a,b \text{ \& } c$ are the roots of this equation, find the value of $\displaystyle \sum_{\text{cyc}} \dfrac{1}{a^3}$ .

Note:

$\displaystyle \sum_{\text{cyc}}$ denotes cyclic summation.