None, because the cubes are solid objects and the tops of the cubes will not hinge together to open like a box.
As to how many cuboid shapes (not counting rotations as different), the answer is 4.
1*1*16
1*2*8
1*4*4
2*2*4
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A rectangular prism that is 4 cubes by 2 cubes is made up of 8 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.
8, one for each corner; all cubes are rectangular.
10
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.