Otis offers to trade it to you for something to get rid of the rats.
Rats are rodents.
So are gophers.
Do you have anything that gets rid of gophers?
In your inventory, you should have gopher repellent, which you attained during your "through the double doors in the Governor's Mansion" escapades.
Give the gopher repellent to Otis, and he'll give you the cake.
