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Heat the oven to 180C/160C fan/gas 4. Line a 12-hole bun tin with paper cases. Put the sugar and butter in a bowl and beat together until light and fluffy. Gradually mix in the eggs and vanilla until combined.
Add the flour, cocoa powder and baking powder to the bowl and mix to make a smooth batter. Fold the milk through to loosen. Divide the mixture between the cases using a spoon. Bake for 20 mins, or until a cocktail stick poked into the centre of one of the cakes in the middle row comes out clean. Leave to cool in the tin for 5-10 mins, then transfer to a wire rack to cool completely
While the cakes are cooling, make the icing. Beat together the butter, icing sugar and cocoa powder in a bowl for 5-10 mins, until you have a smooth, creamy consistency. Add the milk to loosen if needed. Pipe or spread on top of the cooled cupcakes.