Yes you certainly can ice a cake the night before and make sure after you bake the cake and ice the cake to refrigerate it overnight so that bacteria doesn't grow on the cake.
Also wait for awhile until the cake cools down before you ice the cake so that the icing for the cake does not melt.
You can ice the cake at anytime you want too and icing the cake the night before or even a few days before after you bake the cake is fine.
If you need to bake a cake 3 days in advance that can be done as well although cakes are best made either the night before or the same day.
But sometimes we are so busy that we have no time to bake the cake on the same day or the day before so baking the cake a few nights before is okay.
Cakes can be made 3 days in advance and the cake will be okay to eat after that time.
Just make sure that if you do make the cake 3 days in advance to cover the cake and refrigerate the cake to keep any bacteria from growing on it.
You can also ice the cake 3 days in advance or wait until that day to ice the cake which would be better.
Cakes are best served when made the same day or at least one day before so they will be as fresh as possible.
But a cake after 3 days will still be pretty tasty and if you don't have time to make the cake sooner and need to make the cake 3 days in advance then you certainly can do so.
I've done it myself and I've bought cakes from bakeries that were even a week old and they were okay but not as fresh.