Determine all pairs $(x,y)$ of integers satisfying \[(x+2)^4-x^4=y^3.\]
Problem
Source: Bundeswettbewerb Mathematik 2024, Round 2 - Problem 1
Tags: number theory, number theory proposed, Diophantine equation
Source: Bundeswettbewerb Mathematik 2024, Round 2 - Problem 1
Tags: number theory, number theory proposed, Diophantine equation
Determine all pairs $(x,y)$ of integers satisfying \[(x+2)^4-x^4=y^3.\]