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12 cubes
There are infinitely many boxes that will fit 200 inch cubes and have space left over and the question does not exclude such boxes. However, there are 12 boxes that will just fit 200 inch cubes.
One way to find out the number of cubes that can fit inside a rectangular box is to use its volume. Knowing the volume of the cubes and that of the box can give an accurate reading of the cubes that can fit.
72
64 cubes,