Well, here is another interesting set of numbers. These numbers, called the Dudeney Numbers (after Henry Dudeney) have the sum of their digits equal their cube roots.

Interestingly, there are just six of them-(1, 8, 17, 18, 26, 27)

1 = 1 & 13=1

8 = 5 + 1 + 2 & 83 = 512

17 = 4 + 9 + 1 + 3 & 173 = 4913

18 = 5 + 8 + 3 + 2 & 183 = 5832

26 = 1 + 7 + 5 + 7 + 6 & 263 = 1757

27 = 1 + 9 + 6 + 8 + 3 & 273 = 19683

And here are some puzzles by Dudeney which you may want to check out - Puzzles By Dudeney