Let $D _ { k } = \left| \begin{array} { c c c } 1 & 2 k & 2 k - 1 \\ n & n ^ { 2 } + n + 2 & n ^ { 2 } \\ n & n ^ { 2 } + n & n ^ { 2 } + n + 2 \end{array} \right|$. If $\sum _ { k = 1 } ^ { n } D _ { k } = 96$, then $n$ is equal to $\_\_\_\_$ .
Let $D _ { k } = \left| \begin{array} { c c c } 1 & 2 k & 2 k - 1 \\ n & n ^ { 2 } + n + 2 & n ^ { 2 } \\ n & n ^ { 2 } + n & n ^ { 2 } + n + 2 \end{array} \right|$. If $\sum _ { k = 1 } ^ { n } D _ { k } = 96$, then $n$ is equal to $\_\_\_\_$ .