Yes, cake freezes well. In this case, I would slice the cake before freezing, use one sheet of wax paper around it first, and then double wrap each slice in plastic wrap. On top of that, use foil wrap. This should keep it in excellent condition. Defrost in the refrigerator for a while before eating and it should be as good as they day you froze it. Making sure the pieces are well-wrapped and sealed is the most important part of the process.
Please let me know if I can help further!