A Dudeney number is a whole number that is a perfect cube, so the sum of its digits results in the cube root of the number. The name derives from Henry Dudeney, who observed the existence of these numbers in one of his puzzles, Root Extraction, where a retired professor of Colney Hatch postulates this as a general method for the extraction of the root.

There are very few numbers: 1 = 1 x 1 x 1 ; 1 = 1 512 = 8 x 8 x 8 ; 8 = 5 + 1 + 2 4913 = 17 x 17 x 17 ; 17 = 4 + 9 + 1 + 3 5832 = 18 x 18 x 18 ; 18 = 5 + 8 + 3 + 2 17576 = 26 x 26 x 26 ; 26 = 1 + 7 + 5 + 7 + 6 19683 = 27 x 27 x 27 ; 27 = 1 + 9 + 6 + 8 + 3

H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1968, p 36

wiki