We have vegan friends, and I've made a few vegan cakes. I can go one better, I've made vegan GLUTEN FREE cakes! What I usually do is just use a regular cake recipe, but use soy margarine instead of butter, soy milk instead of milk, and egg replacer for the eggs. They've all turned out fine!
Good luck!
i make a chocolate vegan cake that is not that bad. The chocolate really helps to cover the weird taste of no good stuff like butter. Its just flower, sugar, coco powder, oil, baking soda, lemon juice and water. I don't know the exact measurements right now as I am not home. But If you still don't find on on the internet I will be back at my house this weekend. PM if you need it!.
how about a tortilla. Just joking..
rotflmao....oh how I wish I had not just taken a sip of coffee before reading that........ 
I know that you said that you were looking for a white cake recipe, however, I've got a chocolate cake recipe that doesn't have milk, eggs, or butter. It's an old recipe that my grandmother used to make to take to Rodeo's.......(hence the no eggs, butter, or milk......it didn't spoil!)
Let me know if you would like the recipe!
You can try a diet soda cake--maybe white cake with 7up or something along those lines? It's just cake mix and one can of diet soda--you don't add any of the oil, butter, etc., on the back of the box. Fill your cake pan about 2/3 full, and use a heating core of some kind. hth
Probably not, but if they're avoiding those ingredients for calorie control, or because they are vegan out of principle (rather than being vegan for the health benefits), then a diet soda cake works out just fine. It was just another suggestion.
I have a son that had to have a wheat, dairy and egg free birthday cake for his first and second birthdays. I had bought an allergen free cake mix from www.allergygrocer.com. The problem here is that they don't recommend replacing all three. So I ended up with a cake that was more biscuit consistency than cake. But still tasty.
Most egg replacers have wheat, but you can sub a gluten free baking soda and water for an egg. (I forget the qty's). You could also use club soda. I've also heard some people use apple sauce to replace butter.
I have a son that had to have a wheat, dairy and egg free birthday cake for his first and second birthdays. I had bought an allergen free cake mix from www.allergygrocer.com. The problem here is that they don't recommend replacing all three. So I ended up with a cake that was more biscuit consistency than cake. But still tasty.
Most egg replacers have wheat, but you can sub a gluten free baking soda and water for an egg. (I forget the qty's). You could also use club soda. I've also heard some people use apple sauce to replace butter.
This link might be helpfull. They have a whole section about baking with substitutes.
http://www.allergygrocer.com/gluten_free_wheat_free_id235.html
My carrot cake can be made vegan, and it's terrific. Banana cake can be made vegan as well and turn out great. Stay away from cake mixes, because virtually all of them have non-vegan ingredients.
Your going to need a cake that has some moist ingredients that replace the unctuousness of butter, sour cream etc. A cake with finely grated coconut is usually a good bet for a vegan conversion as well.
I'm new around here, but I just wanted to suggest http://www.amazon.com/dp/1569242739/?tag=cakecentral-20 <---this book. I'm fairly certain that a lot of these recipes could be adapted to be used as a full cake and gives good pointers on things to avoid. I'm not vegan (I love cheese waaaay too much), but I really loved this book.
Try this site-
http://www.cs.unc.edu/~kupstas/FAQ_recipes.html#ChocCake
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