Digit Sums of Squares and Cubes If you add up all the digits in 468, you get 4 + 6 + 8 = 18. The square and cube of 468 are 219024 and 102503232, respectively. Interestingly, if you add up the digits...

Digit Sums of Squares and Cubes

If you add up all the digits in 468, you get 4 + 6 + 8 = 18. The square and cube of 468 are

219024 and 102503232, respectively. Interestingly, if you add up the digits of the square

or cube, you get 18 again. Are there other integers that share this property? Write a

program that lists all positive integers k less than 1000 such that the three numbers k, k2,

and k3 have digits that add up to the same number.