The information on the internet is highly unreliable, these websites say that potential remains constant inside conducting solid sphere:
Electric potential inside a conductor
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html
These sites say potential varies as a function of distance:
Integration for finding potential inside uniformly charged solid sphere
which one is it?
In the second case, notice that the sphere is uniformly charged i.e. there is a volume charge present in the medium. But in conductors that certainly cannot be the case. All charges must reside on the outer surface of a conductor. So this is not about a conductor. Potential inside a conductor is unambiguously constant.
To prove that you must understand that electric field inside a conductor is zero. (By inside I mean, in the meat of the conductor, where there is material, not in some cavity.) So, if there was a varying potential inside the conductor, then there would have been a change in potential with distance, creating a gradient in the potential. Now the negative gradient of potential is nothing but electric field, which turns out to be non-zero in case of varying potential. But as mentioned previously, electric field inside a conductor is zero. So our initial assumption must be false. i.e. potential inside a conductor cannot vary.
For further reading study Electrodynamics by David J. Griffiths.
The second case is charged, but not conductive.
If it were conductive, the repulsion between the charges would keep it from remaining uniformly charged. All of the charge would move to the outer surface of the sphere.
