Put the tangelos in a medium saucepan with cold water and bring to the boil, drain - repeat. Do this a total of three times and cool the tangelos. I like to do this the night before I want to cook the cake it makes it a lot quicker the following day just to put the ingredients together. This helps to take any bitterness out of the tangelo rind, and since you are going to use the whole tangelo this is important.
Preheat the oven to 350F and grease and line a 8 inch cake pan. If you use a larger cake pan than this - just adjust cooking time.
Halve your cooked tangelos and remove any seeds. Toss the whole tangelos into the food processor and blend to a pulp, including the skins - do not peel.
Beat the butter, sugar and eggs together in a small bowl with an electric beater until light and fluffy, add to the tangelo pulp and mix together gently.
Stir in the sifted flours and the coconut gently and pour into the prepared cake pan.
Bake for roughly 45 minutes. Test with a skewer, which should come out clean. Stand the cake for 5 minutes - this is important the cake is quite fragile at this stage. While the cake is standing make the syrup.
Place all the ingredients in a small saucepan and stir slowly while warming to dissolve the sugar before the syrup reaches a boil. Once the sugar has dissolved bring to a boil and boil for 3 minutes without stirring. Pour the hot syrup over the hot cake.
Turn with the top side up on to a wire rack placed over a tray with sides. Pour the hot tangelo syrup over the hot cake. It will soak into the cake quite quickly. Collect any syrup that has collected in the tray and place in a small jug for pouring over the cake when you serve it. Serve the cake slightly warm.