What caliber is a Deustche Waffen-und Munitionsfabriken Berlin Gun?

Not possible answer this without more information- you have told us who made the gun (DWM, the German national arms company) and where (Berlin)- but nothing about the gun. While this MAY be an 8mm Mauser type rifle, the 8mm cartridge was made in 2 different versions at different times. The safest route to an accurate answer will be to have a gunsmith examine your rifle. Many military surplus rifles have been rechambered for civilian cartridges different from the original caliber- a gunsmith can tell this.
Not possible answer this without more information- you have told us who made the gun (DWM, the German national arms company) and where (Berlin)- but nothing about the gun. While this MAY be an 8mm Mauser type rifle, the 8mm cartridge was made in 2 different versions at different times. The safest route to an accurate answer will be to have a gunsmith examine your rifle. Many military surplus rifles have been rechambered for civilian cartridges different from the original caliber- a gunsmith can tell this.