Show that $\sum_{N-1}^{k=0} \left | F_{k} \right |^{2} = \frac{2N^{2} + 3N + 1}{6}$ for DFT coefficients $F_{k}$

Question

Let $F_{k}$ be the DFT of the sequence $1, 2, ..., N$. Show that

$$\sum_{N-1}^{k=0} \left | F_{k} \right |^{2} = \frac{2N^{2} + 3N + 1}{6}$$

Any advice is appreciated.