Pre-heat the oven according to the package directions on the cake mix.
Mix the cake according to the package directions.
Divide the cake into smaller bowls according to how many colours you want to use.
Colour each bowl with food colouring until you achieve the colour you desire. You will want to use a drop or two more than you think you need as the colour will be less bright after baking.
Drop the cake batter into a prepared 9x13 pan in random patterns, depending how you want the cake to look. Avoid swirling the batter as it can create muddy colours. Bake the cake according to package directions.
Let the cake cool completely, then use the end of a wooden spoon or other tool, such as a wide chopstick, to poke holes in the top of the cake. You want holes that are about half inch wide.
In a medium bowl, mix one box of the instant pudding with 1 1/2 cups of milk just until it begins to thicken, but is still runny. Use a small tipped piping bag or small spoon to fill the holes with pudding, then spread any remaining pudding over the top of the cake.
Mix 1 cup of milk with the remaining box of pudding just until it begins to thicken, then fold in the frozen whipped topping.
Spread the topping over the cake in an even layer. If you wish you can reserve part to pipe swirls on top of the cake.
Decorate the cake with sprinkles then refrigerate for at least 30 minutes in order to allow the pudding to set.
Slice and serve as desired.