A bit difficult to be certain from the pics (and yes, getting good ones takes practice), but the rifle appears to have a smooth taper barrel. German military barrels were "stepped", with clear "step" at the change of barrel diameter. Sometimes, original barrels were turned, to the preferred sporter taper, but usually a smooth taper barrel means that it has been replaced.
That being the case, get thee to a decent gunsmithy, and have the chamber checked (chamber cast, if in doubt) and the bore measured. IT could be chambered for the standard 8x57mm, or it could be chambered for one of a dozen different European or American wildcat or uncommon cartridges.
Just because an 8mm Mauser round will chamber (and fire) is not an absolute guarantee with a rifle as reworked as that one is.
That being the case, get thee to a decent gunsmithy, and have the chamber checked (chamber cast, if in doubt) and the bore measured. IT could be chambered for the standard 8x57mm, or it could be chambered for one of a dozen different European or American wildcat or uncommon cartridges.
Just because an 8mm Mauser round will chamber (and fire) is not an absolute guarantee with a rifle as reworked as that one is.