Preheat oven to 350° and spray a 9×13 pan.
For the cake, whisk together all of the cake ingredients in a large bowl and pour into the prepared pan.
Bake for 30 minutes.
Remove from oven and let cool for 15 minutes.
While the cake is cooling, prepare the filling. Mix together pudding packet and milk in a medium bowl until smooth.
Using the handle of a wooden spoon (or another similarly sized object), poke holes in the cake and pour the filling over the entire cake.
Cover and chill for around 2 hours, or until the pudding is set.
To prepare the frosting, combine all of the frosting ingredients using an electric mixer. Mix the frosting until it is light and fluffy.
Frost the cake and store in the fridge until ready to serve.
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