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This problem trains for: SAT-I.

Ann, Brian and Cyrus found a box with N cubes of identical size. Each of them made a cubic shape by placing small cubes on top of one another and no cube was left over. Which of the following cannot be N?

Any of the cubic shapes contains a number of small cubes that is a perfect cube. We have to check to see which of the proposed numbers cannot be written as a sum of three perfect cubes:

It is obvious that only 100 cannot be written as desired.