Mix together the sugar, butter, eggs and vanilla in a large bowl with an electric mixer for 5 minutes.
Reduce the speed to low, and add the flour and baking powder, alternating with milk. Then gently fold in the sprinkles and rainbow and white chocolate chips until just combined.
Grease a rabbit-shaped cake pan (purchase one here) with butter, and dust with flour. Spoon the batter into the pan, and bake for 40 minutes at 350F.
Cool the cakes for 15 minutes in the pan, and then invert onto a cooling rack and cool completely.