I was unfamiliar with the "grooms cake" until Dave (the groom) asked me if we were getting a groom cake. I was slightly baffled. Fortunately, we had a friend of the family who wanted to make a contribution to the wedding planning and specifically make the groom's cake, so it was all taken care of. Since it was the groom's cake, Dave got to pick cake flavors and design. It seemed fair, since I didn't give him an opinion on the wedding cake. He is a marine, so the cake design was an Eagle, Anchor, and Globe Marine insignia. I don't remember the cake flavor.
When my sister got married, she made the groom cake for her man. It was the Mustafar scene from Star Wars. It was the groom's favorite Star Wars scene. Pretty cool.
Both times, the cake was served at the reception. I wouldn't do the rehearsal dinner. Only the wedding party is at the rehearsal dinner, meaning no guests can eat and appreciate the cake.