Can you put whipped cream on a cake?

I've done so many times! If you want it to hold up a bit better, I would definitely stabilize it with some gelatin: https://www.cooksillustrated.com/how_tos/8351-stabilizing-whipped-cream

Yes, you can ice a cake with whipped cream. Here's a recipe for chiffon cake with whipped cream frosting: https://www.seriouseats.com/recipes/2018/04/classic-chiffon-cake-with-vanilla-chantilly.html

My understanding is that whipped cream is not very stable, but the recipe above says it lasts for a day. Either way, I think cakes finished with whipped cream should be eaten quickly.