Preheat oven to 350 and grease a 9x9x2 baking pan. Mix cocoa powder and the 3 T of sugar together in a bowl, set aside.
In a large bowl, cream together sugar and butter until fluffy. Add eggs one at a time, beating after each addition.
In another bowl, combine flour and baking powder. In one more bowl, combine milk and vanilla extract. Alternate between adding about 1/3 of the flour mixture and 1/3 of the milk to the butter/sugar mixture until everything is completely combined.
Pour about one third of the batter into the prepared pan. Sprinkle about half of the cocoa/sugar mixture on top. Pour another third of the batter in the pan, top with the rest of the cocoa mixture, finish by layering in the final third of the batter.
Bake for 25-30 minutes or until the cake tests done with a toothpick.