2022 Cayley Problem 13

Two identical smaller cubes are stacked next to a larger cube. Each of the two smaller cubes has a volume of 8. The combined height of the smaller cubes equals the height of the larger cube. What is the volume of the larger cube?

\textbf{(A)}\ 16\quad \textbf{(B)}\ 32\quad \textbf{(C)}\ 125\quad \textbf{(D)}\ 48\quad \textbf{(E)}\ 64

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 Cayley contests here.