Cubesum

Cubesum refers to a computational task in which the sum of the cubes of the digits of a given integer is calculated. The algorithm takes a non‑negative integer, extracts each decimal digit, raises it to the third power, and accumulates the results. The resulting value is often used as a test for special number properties, such as identifying Armstrong numbers (also called narcissistic numbers) where the number equals its own cubesum.

Mathematically, if a number N has decimal digits d₁, d₂, …, d_k, then its cubesum C is defined as C = d₁³ + d₂³ + … + d_k³. For example, the number 153 has digits 1, 5, and 3; its cubesum is 1³ + 5³ + 3³ = 1 + 125 + 27 = 153, confirming it as a 3‑digit narcissistic number. This property generalises to n‑digit numbers where the sum of the nth powers of the digits equals the number itself.

Efficient implementations avoid repeated conversion to strings or arrays by using integer division and modulo operations. Each digit is isolated by the expression digit = N % 10, then N is divided by 10 to remove the processed digit. The process continues until N becomes zero. The algorithm runs in O(log₁₀ N) time and uses O(1) additional memory.

Applications of cubesum calculation appear in coding challenges, numerical puzzles, and educational exercises that illustrate number theory, base‑10 systems, and algorithmic efficiency. In many programming contests, a cubesum function is a common utility for generating or validating Armstrong’s numbers or exploring the behaviour of digit‑power sums.