In my experience, most cake recipes are nut-free unless you decide to add nuts (e.g., carrot cake often has nuts, but it's not required) or a nut extract or paste. My niece is deathly allergic to nuts so I use imitation almond flavoring instead of real almond extract if she's going to eat the cake/cookies.
To avoid contamination by nuts (and almond paste, and peanut and cashew butters, etc.), I use a separate cutting board that can be sterilized in the dishwasher along with knives, spoons, etc.
Boxed cake mixes have to say if they contain nuts or are manufactured in facilities that process nuts.
I often try recipes that I find on allrecipes.com.They are reviewed and I stick to the 4- and 5-star ones.