who typically designs the groom's cake?

His will be served at the rehearsal dinner and a total surprise. I do think he has a clue though. It will be an Xbox or PS4.

Some grooms float ideas if they know it's coming but generally speaking I thought it was down to the bride to sort it.

(perhaps with input from someone like the BM/FSIL/FMIL sometimes?)

I let my DH design his. He loves sports, so when we had our tasting I asked him did he want a Indy Colts or Pacers. He choose the Colts. I hate red velvet but he loves it so that will be his grooms cake flavor.

FH's family is giving him his grooms cake at the rehearsal dinner. I think FH might have a little input, but not much - I think his family is primarily designing it

I'm glad I talked to FH about it because I would have done something fun like a baseball or hunting theme and he didn't want any type of decoration! Just regular icing

ETA: I'm having custom cookies made for him that will be baseball themed that he'll get the morning of the wedding. It's a surprise. I was going to have them at the reception but I was worried that he wouldn't get to enjoy them