2009 Fermat Problem 6

Sixty-four identical cubes are stacked in a 4 \times 4 \times 4 arrangement and then some of the cubes are removed from the front as shown. No cube hidden from sight has been removed. How many cubes remain in the arrangement?

\textbf{(A)}\ 46\quad \textbf{(B)}\ 40\quad \textbf{(C)}\ 52\quad \textbf{(D)}\ 55\quad \textbf{(E)}\ 49

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