No, Mario Götze is not the most expensive German player ever. He was sold from Borussia Dortmund to Bayern Munich for €37 million, but this is not the most expensive transfer involving a German player. That record is held by Mesut Özil, who was sold from Real Madrid to Arsenal for €42.5 million in 2013.
The Amazing Journey of Mario Götze: How Well Do You Know the German Football Sensation?