Preheat oven to 325 degrees. Oil three 8-inch round cake pans.
Beat eggs in large bowl. Add sugars; beat until light and fluffy. Add oil and mix well with whisk. Add dry ingredients; beat until smooth. Stir in remaining ingredients. Pour batter into oiled pans. Bake 40 minutes. Cool slightly before frosting.
Layers may be frozen for use at another time.
Cream Cheese Frosting
1/2 cup butter, softened
8 ounces cream cheese, softened
1 pound confectioners' sugar
3 teaspoons vanilla
Mix all ingredients together until smooth. Spread frosting between cake layers and on top and sides.