Add half of the dry ingredients to the butter and sugar mixture and blend, then add half of the wet ingredients. Repeat this process until all the ingredients are combined.
Pre-heat the oven to 350°, and line the bottom of at least two 9-inch diameter cake pans with wax paper. (Use as many layers as you like for your own cake.) Divide the batter between pans, and bake until a toothpick inserted into the cake comes out clean, about 25 minutes. Cool cakes in pans for about 10 minutes, then turn them out onto a wire rack and peel off the wax paper. Let the layers cool completely before frosting.
In a bowl, beat together the cream cheese and butter until mixed, then beat in the sugar. Finally, add the vanilla.
Place one cake layer, bottom side up, on a platter. Spread with frosting, then top with another layer, bottom side down. Repeat with each layer, then spread the remaining frosting smoothly over the top and sides of the cake.