Number spiral diagonals

Starting with the number \( 1 \) and moving to the right in a clockwise direction a \( 5 \) by \( 5 \) spiral is formed as follows:

\[ \begin{gather} \color{red}{21}\ 22\ 23\ 24\ \color{red}{25}\\ 20\ \ \ \color{red}{7}\ \ \ 8\ \ \ \color{red}{9}\ 10\\ 19\ \ \ 6\ \ \ \color{red}{1}\ \ \ 2\ 11\\ 18\ \ \ \color{red}{5}\ \ \ 4\ \ \ \color{red}{3}\ 12\\ \color{red}{17}\ 16\ 15\ 14\ \color{red}{13}\\ \end{gather} \]

It can be verified that the sum of the numbers on the diagonals is \( 101 \).

What is the sum of the numbers on the diagonals in a \( 1001 \) by \( 1001 \) spiral formed in the same way?