Preheat oven according to the instructions on the cake mix box.
Prepare and bake the red velvet cake in a 9x13-inch baking dish according to package directions.
Let the cake cool for about 15 minutes, then use the handle of a wooden spoon to poke holes all over the cake.
In a bowl, whisk together the pudding mix and cold milk for 2 minutes until it starts to thicken.
Pour the pudding over the cake, gently pressing into the holes. Spread evenly.
Refrigerate for at least 2 hours to set.
Top with whipped topping and sprinkle with red sprinkles or crumbs before serving.