When frosting a cake you can frost the cake as far as 3 days in advance of serving or eating the cake.
However if it's gonna be more than 1 day before eating or serving the cake it would be best to just bake the cake and then store the cake in the refrigerator and then on the day you plan to serve it then take it out and add the frosting.
For best results when icing or frosting a cake you should allow the cake to cool down completely.
If you add frosting or icing to a warm or hot cake then the frosting or icing can melt and run off the cake.
Although it does not have to be completely cool but give the cake some time to cool down for at least 20 minutes after removing the cake from the oven and then put the frosting on the cake.
The cake doesn't have to be cooled down completely before frosting it but make sure you allow the cake to cool down at least some before frosting the cake.
If you apply the frosting on the cake while it's still hot the frosting can melt which would make the cake not as good and you'd have to apply some more frosting.
I always wait until the cake gets to room temperature before frosting the cake and never had an issue with melting frosting.
A cake should cool for 30 minutes to 60 minutes before frosting the cake as the cake even being warm can sometimes melt the frosting.