Place your 4 clementines (whole and un peeled) in a small saucepan and cover them with water. Bring them to the boil and then simmer them for 1 hour. Strain them and leave them to cool.
Preheat your oven to 180C / 350F / Gas mark 4.
Lightly grease a 20 cm springform cake tin.
Cut your cooled boiled clementines, keeping the peel on in half and pulse in your food processor until they are finely chopped but not quite pureed.
In a jug combine all your dried fruit give them a quick mix and then add the rum if using if not add your fruit juice. Place aside.
In your mixing bowl cream the butter and sugar together until pale and light.
Add a little of the beaten egg at a time until all the egg is combined.
Add the polenta and baking powder to the creamed mixture and fold in.
Add the dried fruit and rum (or juice) to the cake batter and fold in.
Pour the batter into your prepared cake tin, level out the top and pop into the oven.
After 30 minutes you need to reduce the temperature of your oven to 160C / 315F / Gas mark 3
And continue to bake your cake for a further 40 minutes. For the final 20 minutes keep a close eye on your cake if its starting to look brown enough on top cover it with tin foil and continue baking for the full amount of time.
Once the time is up take your cake out of the oven and allow it to remain in its tin to cool for 30 minutes.
After 30 minutes gently remove the cake from its tin and allow it to fully cool on a wire rack.
While your cake is cooling you can be prepping the candy clementine slices.
Add the sugar and water to a medium sized pan and gently heat until the sugar is dissolved, stirring often. Then turn the heat down to a low simmer.
Slice the clementines thinly about 5 millimetres thick and place them in the hot sugar syrup and allow them to simmer for an hour.
You are waiting for them to go translucent and glossy.
After the hour carefully remove the slices and allow them to cool on a sheet of greaseproof paper.
Dust the whole cake with icing sugar and arrange the clementine slices slightly overlapping over the top of the cake.
This cake should keep for up to 2 weeks, when kept in an airtight container.