\[\frac{3 + 3n + 3n^{2}}{n^{3} - 1} =\]
\[= \frac{3 \cdot \left( 1 + n + n^{2} \right)}{(n - 1)\left( n^{2} + n + 1 \right)} =\]
\[= \frac{3}{n - 1}\]