When baking a cake using already made cake mix in a box you add at least 3 eggs as well as some vegetable oil and then some water and mix the cake mix up using either an electric mixer or hand mixer.
I prefer to use an electric mixer to mix the cake mix up.
If you want to add more than 3 eggs you can do so but 3 eggs is minimum to make the cake perfect.
However if you cannot have eggs you can make the cake without eggs if you want too or need too.
You can use some applesauce in place of the eggs if you want too but I've made cakes without any eggs or applesauce and it turned out okay for me.
You can use milk instead of water as well to help with the taste of the cake when you don't use eggs.