# How to prove a cube minus a cube is never a cube (in whole numbers) [duplicate]

How to prove $x^3-y^3\neq z^3$ where $x$, $y$, and $z$ are whole numbers (integers greater than zero)?

Actually, This is a special case of Fermats Last theorem where $n=3$ You can find the proof here
Proof for $n=3$ fermats last theorem
In general, Fermats last theorem states that there is no integer solutions for the equation $x^n + y^n = z^n$ where $n \geq 3$