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Choice D is correct. The volume, $V$, of a cube can be found using the formula $V=s^3$, where $s$ is the edge length of the cube. It's given that a cube has an edge length of $41$ inches. Substituting $41$ inches for $s$ in this equation yields $V={41}^3$ cubic inches, or $V=\mathrm{68,921}$ cubic inches. Therefore, the volume of the cube is $\mathrm{68,921}$ cubic inches.

Choice A is incorrect. This is the perimeter, in inches, of the cube.

Choice B is incorrect. This is the area, in square inches, of a face of the cube.

Choice C is incorrect. This is the surface area, in square inches, of the cube.