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Preheat oven to 350 degrees F.
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Grease and flour a 9x9 inch pan or line a muffin pan with paper liners.
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In a medium bowl, cream together the sugar and butter.
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Beat in the eggs, one at a time, then stir in the vanilla.
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Combine flour and baking powder, add to the creamed mixture and mix well.
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Stir in the milk until batter is smooth.
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Bake for 30 to 40 minutes, or until golden brown and toothpick comes out clean.