Cake – How to make cake batter from scratch without butter

A 9" round pan that is 1 1/2" deep takes 6 cups of batter, while one that is 2" deep takes 8. That's for totally full to the brim. This source says about the amount of batter from a box:

An average 2-layer cake mix yields 4 to 5 1/2 cups of batter.

and should have a bunch of helpful guides to using batter for non-standard pans.

For a boxed cake either type of cooking fat should render a similar result. The final flavor will be a little different, but it shouldn't make a huge difference and probably won't be much different than a mix that calls for oil in the first place.

If you wanted to keep the flavor similar while avoiding dairy you could try using butter flavored shortening instead of oil.