2021 Gauss 8 Problem 24

Jonas builds a large n \times n \times n cube using 1 \times 1 \times 1 cubes each having the net shown. What is the smallest value of n for which the sum of the exterior faces of the n \times n \times n cube can be greater than 1500?

\textbf{(A)}\ 9\quad \textbf{(B)}\ 11\quad \textbf{(C)}\ 12\quad \textbf{(D)}\ 13\quad \textbf{(E)}\ 16

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.