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64

I may be interpretting the clues wrong, but the only 2 cubes that are 2 digits are 27 and 64.

I assumed it meant you add 3 to get the cube, meaning the answer would be 24 or 61, but neither of those add to make 13.

So assuming the other way, that you add 3 to the cube and then the digits make 13, adding 3 to 64 you get 67, 6+7=13

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