If there's a phone number it's usually faster to call and ask what their policies are. If you tell them it's a one-time use for a fan, or an alum of the college, they might be nice about it.
The other question is whether you should get the permissions, or whether you want to have the client do it. In general you should probably do it, since you'll usually need something in writing. I had a client get permission from a children's cartoon show, and they still needed to talk to me about it, so doing it yourself takes out the middleman.
In my personal experience, colleges will usually let you use their logos for alumni cakes. Pro football teams are relatively easy to work with, but pro baseball teams are a bunch of making-you-jump-through-hoops jerks. Your experience may vary.
A lot of companies that do cartoons will not give out permission, but some of the smaller ones will. Forget anything Disney unless you want to pay a ton of money for their license. In cases like that, just do a cake that has similar colors as the main theme of the cartoon, then have the client buy a toy to put on it. That keeps you out of the copyright loop.
Kara Buntin owns A Cake To Remember LLC, custom wedding cakes in Richmond VA