Preheat the oven to 180°C.
Trim the roots from the beetroot and wrap each beetroot in foil.
Bake the beetroot for 50-60 minutes, or until you can easily insert a knife into them, then unwrap and set aside to cool.
Once cooled, peel the beetroot (the skin should come off quite easily) and cut each beetroot into wedges.
Process the beetroot and raspberries in a food processor until texture resembles jam, then transfer to a large mixing bowl.
Reduce the oven to 170°C and line a 15cm x 15cm square pan with baking paper.
Add the remaining ingredients to the mixing bowl and stir to combine.
Press the mixture into the pan, smoothing the top with the back of a spoon, and bake for 35-40 minutes, or until cooked through.
Allow the cake to cool in the tin for 5-10 minutes, then transfer to a wire rack to cool completely.
Once cooled, combine the icing ingredients in a small mixing bowl,
then carefully spread over the cake with a warm knife.
Place the cake in the refrigerator to set before you trim the edges and cut into pieces.
Return to the refrigerator until you are ready to serve.