In reply to a Mama's Dish user's question on how to preserve cakes, I did some research and have put together some methods of storing/preserving cakes.
Cakes are best stored at room temperature but depending on the frosting, if it has fruits in it, or custard, then the methods or ways of storing them will differ a bit. These methods work for any kind of cake: layer cake, sheet cake, pound cake, quick breads, and even cupcakes.
The cake types will be broken down into frosted and unfrosted, cut and un-cut cakes.
Unfrosted and Un-Cut Cake
Wrap these tightly in plastic wrap, top, sides, and bottoms, so the plastic is touching the sides of the cake (that is to say, don't just drape the plastic over the top). Second to this, go for a plastic bag with a "zip-lock" type seal. Store these wrapped cakes on the counter at room temperature, and they'll keep for about a week before starting to stale on you. Oil-based cakes tend to keep a day or two longer than butter-based ones.
Frosted and Un-Cut Cake
The frosting actually acts like plastic wrap here, protecting the cake from air and moisture in the environment. A frosted cake can be kept at room temperature for 4-5 days. Cover it with a cake keeper or an overturned bowl to protect it from dust, pet hair, and other things in the air (plastic wrap isn't necessary and would smoosh up the lovely frosting). A cake expert says that she actually keeps her frosted cakes in the microwave!
Cut Cake, Frosted or Unfrosted
Stella Parks (a pastry chef at Lexington restaurant Table 310 and the brains behind the phenomenal BraveTart blog.) says to think of sliced cake as a living organism. As soon as you make a cut, moisture begins to escape and cause the cake stale more quickly. If you can, cover the sliced edges with more frosting to protect the cake from moisture loss. Otherwise, press a piece of plastic wrap directly onto the sliced side and make sure it sticks. Then proceed with covering and storing the cake as for the un-cut version. Cut cake keeps for a little less time, about 3-4 days.
When to Refrigerate Cakes
Cakes both frosted and unfrosted, cut and un-cut, are perfectly fine at room temperature for several days. Refrigeration is only necessary if your apartment gets very hot during the day (As Stella Parks says, "High moisture + high sugar + high temp = bacteria feeding frenzy") or if you're making a cake that won't be served for more than three days, like when baking cake ahead for a party or special occasion.
To refrigerate, wrap unfrosted cakes in plastic to protect it from absorbing any weird fridge smells and to protect it from drying out, and then unwrap it to warm up on the counter before serving. For frosted cakes, chill the cake uncovered for fifteen minutes to harden the icing, then wrap it in plastic wrap.
To keep cakes for longer than a week, try freezing them.
Resources: theKitchn