Find all the $4$-digit natural numbers, written in base $10$, that are equal to the cube of the sum of its digits.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2020 p1
Tags: number theory, sum of digits
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2020 p1
Tags: number theory, sum of digits
Find all the $4$-digit natural numbers, written in base $10$, that are equal to the cube of the sum of its digits.