Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13 inch baking dish.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the Cheddar cheese. Combine the flour and baking powder; stir into the batter alternating with the milk until smooth. Pour into the prepared pan.
Bake for 45 minutes in the preheated oven, or until a knife inserted into the center of the cake comes out clean.