  A difficult classical problem in the qualitative theory of differential
systems in the plane $\mathbb{R}^2$ is the center-focus problem, i.e. to
distinguish between a focus and a center. Another difficult problem is to
distinguish inside a family of centers the ones which are global. A global
center is a center $p$ such that $\mathbb{R}^2\setminus\{p\}$ is filled with
periodic orbits. In this paper we classify the global centers of the family of
real polynomial differential systems of degree $3$ that in complex notation
write $$
i\dot{w}=w-A_3\overline{w}^2-A_4w^3-A_5w^2\overline{w}-A_6w\overline{w}^2, $$
where $w=x+iy$ and $A_k\in\mathbb{C}$ for $k=3,4,5,6$.
