Once cake has cooled, break it into pieces and place in a bowl. Add frosting. Using your hands mix everything together until it's cohesive. If you prefer, you can do this in the bowl of a stand mixer and use the paddle attachment to mix to combine.
Put candy melts or white chocolate in a bowl and melt in the microwave (I recommend using 50% heat for 1 minute and then stirring before placing back in the microwave and using 50% heat for 30 seconds. Take out and stir. Continue until chocolate is melted). If you prefer to use a double boiler, you can. I like to work with about 1 cup of candy melts at a time and simply add more to the bowl and re-melt when needed. If chocolate hardens while you're working, simply put the bowl back in the microwave to re-melt.
Spoon some of the chocolate into the bottom your cakesicle mold and using a small off-set spatula or a pastry brush, evenly distribute chocolate along the entire bottom of the mold and up the sides. Take one of the popsicle sticks and insert it into the mold and then remove it. This is simply to ensure that the chocolate doesn't harden over the opening as you'll need to insert the stick later.
Place molds in the fridge for 5 minutes to harden. Upon removal, check sides of molds and if the chocolate looks thin, brush a little more on and let harden again.
Put a little more than 1 Tbsp of cake mixture over the hardened chocolate in each mold and press down. Make sure it's nice and smooth with no crumbs and that it's just below the lip of the mold. Insert a popsicle stick into each mold and press down on the cake again.
Coat the cake with more melted white chocolate to cover the backs of the cakesicles. Place in the fridge for 5 minutes to harden.
Gently remove cakesicles from their molds. You'll have to wiggle them a little and take care when pushing the popsicle stick out. Repeat with molds.
Brush a little more melted chocolate on the cakesicles to adhere bunny ears, sprinkles, etc. Utilize an edible marker to draw eyes and mouth on the cakesicles.