I made a chocolate beetroot cake in 2015 that used raw beetroot, this one uses cooked beets and I think that helps to give the cake a real fudgy texture. Kids won't even know there's beetroot in there! This recipe is from Marian Keyes' Saved By Cake, but I used less sugar.

250g cooked beetroot
100g dark chocolate
125g butter
1c muscovado or brown sugar
3 eggs
225g flour (I use spelt)
30g cocoa powder
pinch salt

Preheat oven to 180C and line a 20cm cake tin with baking paper. Grate the beetroot or blitz in a food processor.
Melt the chocolate and set aside. Cream the butter and sugar and add the eggs. Sift in the flour, cocoa powder and salt into the butter mixture.
Stir in the beetroot and chocolate. Pour into the cake tin and bake for 35-40 min until cooked through. Test with a skewer - if it comes out clean it's ready. Place the tin on a wire rack and when the cake is completely cool, take out of the tin.
I made the icing with 100g icing sugar, 20g butter and 1 Tbs cocoa powder.