Here is a basic recipe for a cake that does not call for eggs. I hope this is what you are looking for. I have not tried this recipe so I hope it turns out well for you.

VEGAN CAKE RECIPE
From: rec.food.recipes Smith Trim, Inc. smithtrim
Serves 8

DRY INGREDIENTS:
1 1/2 cup unbleached flour (I use unbleached organic flour)
1 cup natural sugar
1 teaspoon baking soda
1/2 teaspoon salt
WET INGREDIENTS:
1 cup cold water
1 tablespoon vinegar
1/4 cup vegetable oil, applesauce or a combination of the 2
1 teaspoon pure vanilla

Preheat oven to 350 degrees F. Lightly grease an 8 or 9 inch baking dish. Set aside.

In a large bowl, combine the dry ingredients; set aside.

In a small bowl (or in a 2 cup measuring cup) mix wet ingredients together. Add wet ingredients to the dry and mix with a fork or an electric mixer until well mixed. Pour into prepared pan.

Bake for 30-35 minutes.

VARIATIONS:

CHOCOLATE CHIP CAKE:
Sprinkle 1/3-2/3 cups of chocolate chips on top of the cake before baking.

CHOCOLATE CAKE:
Add 1/4 cup cocoa powder to the dry ingredients. For double chocolate cake, sprinkle some chocolate chips on top of the cake before baking. Try using almond extract instead of vanilla for a nice flavor.

SPICE CAKE:
Add 1 tsp cinnamon, 1 tsp allspice, 1/2 tsp ground cloves, and 1/4 tsp nutmeg to the dry ingredients. Omit the vanilla from the wet ingredients.

GINGER MOLASSES CAKE:
Reduce sugar and water to 3/4 cup. Add 1 tsp cinnamon, 1 tsp allspice, 1-3 tsp ginger (or 1 Tbsp fresh grated ginger) to the dry ingredients. Add 1/4 cup molasses to the wet ingredients and omit the vanilla.

BANANA CAKE:
Reduce sugar to 2/3 cup. Instead of 1 cup water, use 1 cup mashed banana and a little nondairy milk if the batter is too thick.