7. The numbers $1,2,3, \cdots, k^{2}$ are arranged in the following way:
$$
\begin{array}{cccc}
1 & 2 & \cdots & k \\
k+1 & k+2 & \cdots & 2 k \\
\vdots & \vdots & \cdots & \vdots \\
(k-1) k+1 & (k-1) k+2 & \cdots & k^{2}
\end{array}
$$

Select any one of these numbers and strike out the row and column in which it lies. After doing this $k$ times, the sum of the $k$ numbers taken is $\qquad$
7. $\frac{1}{2} k\left(k^{2}+1\right)$