Preheat the oven to 170°C (338°F).
In a bowl, mix eggs and sugar.
Add melted butter and milk, then mix well.
Sift in cake flour, baking powder, and cocoa powder, and mix evenly.
Add espresso and blend thoroughly.
Pour the batter into a pound cake mold and smooth the surface.
Bake in the oven for 40 minutes.
Let cool, then remove from the mold to finish.