Preheat the oven to 350 F or 180 C and grease a 6-cup bundt pan (or a loaf pan) with butter. Coat with flour to prevent sticking unless you use a silicone pan.
In a bowl, cream together the butter and sugar with a whisk or electric mixer until light and fluffy (several minutes).
Whisk in the eggs and vanilla until well-incorporated. The longer you beat these ingredients, the fluffier your cake will be.
Blend in the baking powder, baking soda and salt.
Add the flour in three additions, alternating with the yogurt- but ending with the flour.
In a small bowl, mix the cocoa powder with 2 tbsp hot water, until a smooth paste is formed.
In another small bowl, dissolve the instant espresso powder with 1 1/2 tbsp hot water.
Divide the cake batter evenly into three parts- keep 1 part in the same bowl you made the cake batter and distribute the other 2/3 of the batter among the coffee and cocoa bowls. Fold to combine.
You should end up with 3 different flavors of cake batter.
Spoon dollops of batter into your prepared pan, alternating with each flavor so that each kind of batter is distributed throughout the pan.
Bake for 55-60 minutes or until a toothpick inserted comes out clean or with a few moist crumbs. The top of the cake should be golden. Cool completely for around an hour, then invert onto a cake plate.