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0, 1 and 64 are three numbers that qualify.
Answer: 1, 64, & 729
All integers have a perfect square and a perfect cube. For example: -22 = 4, -23 = -8, -12 = 1, -13 = -1, 02 = 0, 03 = 0, 12 = 1, 13 = 1, 22 = 4, 23 = 8, 32 = 9, 33 = 27, etc.