Most cakes freeze extremely well--especially cakes that are not iced, such as bundt cakes.
Wrap the cake in plastic wrap, then aluminum foil, and freeze. For cupcakes or slices, you can put them in a freezer bag.
If you are going to freeze a whole cake, it is better to frost it after thawing, as the icing can be tricky.
If you have icing, you can put the cake in the freezer long enough for the icing to br firm, and then wrap and freeze--however, thawing can be tricky as you might get a bit of condensation, which can affect the texture of the frosting.
EDIT in response to question about a plastic box, and why the double layering:
- Boxes consume space extra space, often at a premium in a freezer, and offer air gaps in which freezer burn is more likely.
- Not all plastic is food-safe.
- The food-safe plastic wrap is for direct contact with the cake but is gas permeable. I suppose you could just go directly to foil, but things are more likely to stick to it.
- The foil provides a gas and moisture barrier (and light, but that is less of a problem in the freezer).
- The direct contact with the with the cake eliminates the air gaps, making freezer burn much less likely.