A Dudeney number is a perfect cube for which the sum of the digits equals the cube root. The classic example is \(512 = 8^3\), and \(5 + 1 + 2 = 8\). There are exactly six of them in base 10: 1, 512, 4913 (\(17^3\)), 5832 (\(18^3\)), 17576 (\(26^3\)), and 19683 (\(27^3\)).
They're named after Henry Dudeney, England's greatest puzzle composer, who posed the cube-root–digit-sum puzzle. Because the digit sum of an \(n\)-digit number grows far slower than its cube root, the list is provably finite and short.