Place chocolate cake mix, water, vegetable oil, and eggs in a mixing bowl. Beat with an electric mixer on medium speed until thoroughly combined, about 2 minutes.
Fill prepared muffin cups 2/3 full with batter.
Bake in the preheated oven until a toothpick inserted into the center of a cupcake comes out clean, 19 to 23 minutes.
Allow cupcakes to cool thoroughly.
Beat the 2 packages of pudding mix with milk in a bowl using an electric mixer until thickened, about 2 minutes.
Beat thawed whipped topping into pudding mixture to make a creamy filling.
Spoon about 1 1/2 cup chocolate pudding filling into a pastry bag fitted with a large piping tip.
Press the piping tip into the center of each cupcake and fill cupcake with about 1 1/2 tablespoon of pudding mixture.
Spoon a heaping tablespoon of remaining pudding mixture about 1 1/2 inches across into the center of each cupcake to make a nest. Press chocolate sprinkles into edges of the nests; place 3 mini chocolate eggs into each nest.