Billy - gotta disagree a bit with Val, on a point or two. It is true the American ammo makers have 'dissed' and downloaded the 8mm, but not out of concern for the two different bore diameters, both a full World War apart, more out of concern to hype and sell the American designated calibers. The 8mm Mauser doesn't give up anything to the 06, period. You can find 150 gn and 170 gn bullets for the 8mm, both of which can be loaded to the same or better than the 06. Vhita-Vhoury Oy has loadings (European) for the 8mm that put the 170 grn out better than the 180 gn 06, and the Sellier and Bellot ammo comes with a 196 gn sp that clocks at almost 2600'/sec. You have to handload the 200 gn 06 to do that.
All of this is just about the caliber, not your rifle, and Val is quite correct about the different bore dimensions and that you need to find out more about your particular rifle for safety's sake. It might be a wartime (WWII) K98 Mauser, looser'n a goose but strong as bull. Or, you could have something else. Get it checked out as to caliber, model, headspace, bore quality and then collector value. If it's a shooter, use it and enjoy it. HTH. Mikey.