Dudeney number

A Dudeney number is a special kind of integer that is both a perfect cube and the sum of its digits equals the cube root of the number itself. In mathematical terms, a Dudeney number \( n \) satisfies the condition: \[ n = a^3 \quad \text{and} \quad \text{sum of the digits of } n = a \] where \( a \) is a positive integer.