Preheat oven to 350 degrees. Spray a 9x13 cake pan with nonstick cooking spray.
Combine the water and espresso powder. Heat for 1 minute in the microwave. Stir well.
In a large bowl, combine the cake mix, espresso, oil, and eggs. Mix well. Pour into prepared cake pan and bake according to package directions.
In a small bowl, combine kahlúa and sweetened condensed milk.
Once done, remove from the own and poke holes in the top of the cake {I used lollipop sticks}. Pour kahlúa mixture on the top of the cake and refrigerate until cooled.
To make the frosting, melt the butter over medium heat. Whisk in the cocoa and bring the mixture to a boil. Remove from heat and whisk in the vanilla and milk. While whisking continuously, add powdered sugar in 1 cup increments. Spread over cooled cake. Let sit for 10 minutes before serving.