If you are using homemade buttercream, you definitely want to store your finished cake in the refrigerator. Take the cake out at least 30 minutes before you intend to slice and serve to allow the buttercream to soften. If using store-bought icing, refrigeration isn't necessary if you're serving the cake the same or next day. Leftovers should be wrapped tightly or placed in an airtight container and stored in the refrigerator.