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Power Play
Some numbers are both the square of an integer and the cube of an integer. In the obvious cases 0 and 1, it concerns the same integer. But there are also cases where numbers are the cube of a smaller integer and the square of a larger integer.
Challenger
Determine the next 3 numbers for which this applies. What's the largest number among them?
Mastermind
From the above, it follows that the difference between two cubes can be a square. That is true for all these found numbers with 0 as the other cube. But can the difference between two cubes also be a square if both cubes are greater than 0? If you think it is not possible, answer 0. If you think it is possible, give the smallest square that is the difference between two cubes.