You can make or bake a cake a few days in advance of eating or serving the cake.
But if you want the freshest cake it's best to make or bake the cake the same day as you're serving it or eating it or at least one day in advance.
I personally would not make a cake any longer than 1 or 2 days in advance because the cake begins to go stale after a few days.
It doesn't take too long to bake a cake but I would bake it the day before you plan to serve it so that the cake will be fresh and more tasty.
If you plan to buy say a birthday cake it's best to buy the birthday cake a day before or the same day so that it will be the freshest.
So if I were making a cake especially for a birthday then I would make it the day before or the same day depending on how much time I have before it's ready to be served or eaten.