I have a few cakes for this weekend and started baking ahead of time (Thursday) when I realized that the chocolate cake with Bavarian is for Sunday. How long will this cake be good for if I put it in the refrigerator?

Sunday is this weekend. Freezer, refrigerator, or on the counter at room temperature... chocolate cake layers will still be good a lot longer than three days no matter what you do with it.
(Am I missing something? If you're going to finish it ahead of time, with perishable filling/icing, it won't go bad in the refrigerator within 3 days.)