Preheat oven to 350 degrees. Cream together butter and sugar until light and fluffy. Beat in the eggs at high speed until very light and fluffy. Sift together flour and baking powder, then fold into batter. Stir in vanilla. Pour batter into a buttered 8" square cake pan and bake for 20-30 minutes, until light golden brown, and cake begins to pull away from sides of pan.