For storage, cover the cake and store at room temperature after frosting. If you cannot find a container that is tall enough, you can store the cake separately and make the frosting immediately before you intend to serve it. Store leftover cake in an airtight container in the fridge, for up to 3 days. You can refer to these tips
on storing a cake for longer periods of time, but I always prefer to serve the cake the same day I make it, for the freshest flavor.