According to the Deusche Bahn, the trip will take 6 to 6-1/2 hours, with trains departing on the odd hours. I'd take the train on this route, but you might check for cheap flights on skyscanner.com .
The rail fare can climb well above 100 euros per person, but significant savings are available if you buy your tickets really early and choose the non-refundable/non-changeable Savings Fare.
There are some overnight trains (use link I've provided), but all take over 11 hours, seem to come with 3- or 4-hour layovers and apparently do not have any form of sleeper car. Perhaps I've missed a better option, but by the time you paid for something better than a couchette berth--if available--you'd probably exceed the cost of a decent (and far more comfortable) hotel room in Berlin.