It's too bad that the Czech train hack doesn't seem to work any more: There's a train from Berlin to Prague that stops in Dresden. It used to be much cheaper to book the trip Berlin-Dresden with České dráhy, compared to the price you get with DB.

I think you also had to make it an international ticket to make it work, booking the journey from Berlin to the first station after the border. And then just leaving the train early, at your intended destination.