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1331 and 2197
There are a total of 5 positive three-digit perfect cubes that are even. To find this, we first determine the range of three-digit perfect cubes, which is from 46 to 96. Then, we identify the even perfect cubes within this range, which are 64, 216, 512, 729, and 1000.
The integer cubes with cubes less than 2000 are: 13 = 1 23 = 8 33 = 27 43 = 64 53 = 125 63 = 216 73 = 343 83 = 512 93 = 729 103 = 1000 113 = 1331 123 = 1728
There are two sets of two numbers that have cubes that add up to 1729 are {1, 12} : 1³ + 12² = 1 + 1728 = 1729 {9, 10} : 9³ + 10³ = 729 + 1000 = 1729
10001