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Since there are so few options, trial and error/enumeration would be the way to go here.

The 2-digit squares are: 16, 25, 36, 49, 64, 81, 100. The 2-digit cubes are: 27, 64.

The only place where the difference between two of these numbers is 2, occurs between 25 and 27, thus the 2-digit number asked for is 26.

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Q: What is a 2 digit number that is one more than a square number and 1 less than a cubic number?
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