4 of them can.
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A 41 inch cube is 41X41X41 inches. 413=68921 cubic inches. A 41 inch cube can be cut into 68921 one-inch cubes.
Eight 4 inch cubes are needed to build and 8 inch cube.
The 3 foot square box contains 46,656 cubic inches. The 3 inch square cube has 27 cubic inches. The division of 46,656 by 27 yields 1728 3x3x3 cubes inside the larger one.
8
27 of them.