10. The volumes of seven cubes of different sizes are $1$, $8$, $27$, $64$, $125$, $216$, and $343$, respectively. They are stacked vertically to form a tower, with the volume of the cubes decreasing from bottom to top. Except for the bottom cube, the bottom surface of each cube is completely on top of the cube below it. The surface area of the tower (including the bottom) is ( ).
(A) 644
(B) 658
(C) 664
(D) 720
(E) 749
10. B.

From the problem, we know that the edge lengths of each cube are 1, $2, 3, 4, 5, 6, 7$.
Therefore, the required surface area is
$$
6 \sum_{n=1}^{7} n^{2}-2 \sum_{n=1}^{6} n^{2}=840-182=658 \text {. }
$$