For the frosting: Mix the cocoa powder, espresso powder and hot water in a saucepan and bring to a boil over medium heat. Add the evaporated milk, sugar, butter and salt and cook until thick, 3 minutes. Remove from heat and stir in the vanilla paste. Let cool completely, then chill in the refrigerator for 15 minutes.
For the cake: Preheat the oven to 350 degrees F. Butter and flour six 8-inch round cake pans.
Mix the cake batter according to cake mix package instructions. Measure out how much batter you have and then divide it by six. Pour the portioned batter into the cake pans; the layers will be thin, about 1/4-inch in height. Tap the pans on the counter for even baking.
Bake for 7 to 10 minutes, keeping a close eye on the cakes, until cooked through. Remove from the oven and cool on a rack in the pan.
Assembly: Add a small dollop of frosting to a cake stand or cardboard cake round and then set a cake layer on the stand. With an offset spatula, spread the top of the layer with about 1/4 cup of the frosting. Continue building the cake, spreading frosting between each layer. Once all the layers are assembled, leave the top unfrosted. Refrigerate the cake for 30 minutes to allow the frosting to set. Then frost the top and refrigerate for another 30 minutes to set before serving.
It's best to start with the frosting first before making the layers. If you do not have six cake pans, you can clean the pans and repeat until all the batter is used and you have six layers.