Magma in which cubes are well-defined

Definition
A magma $$(S,*)$$ is termed a magma in which cubes are well-defined if it satisfies the following equivalent conditions:


 * For every $$x \in S$$, $$x * (x * x) = (x * x) * x$$.
 * Every element of $$S$$ commutes with its square.

The value $$x * (x * x)$$ is termed the cube of $$x$$ and is denoted by $$x^3$$.