How to have a color transition material on a mesh? Basically, I have a simple sphere and I want the the most inner part of the sphere, so the center of it, to be once color and to gradually transition to another color and it approaches the most outer part of the sphere.

Can you achieve this effect without having to rely on placing another sphere inside?
Based on  Diogo Valadares's comment, you can indeed use a fresnel node + color ramp to achieve this effect. Below, I attach a fresnel node to a color ramp with a mapping node in between, giving me a transition between red and blue from the inside to the outside. 



Depending on what kind of transition you want, the fresnel node may not be perfect (you can see that on the very edge, the transition is a bit too sharp), but by playing around with the constants in the mapping node you can get a sharper or smoother transition.