\prod_{k=2}^n \frac{(k^2+k+1)}{(k^2-k+1)}=\frac{7}{3}\cdot\frac{13}{7}\cdot\frac{21}{13}\cdot\frac{31}{21}\cdot\ldots\cdot\frac{(n^2+n+1)}{(n^2-n+1)}=\frac{(n^2+n+1)}{3}