Place the whole clementines in a saucepan with a lid. Cover them with an inch of water and bring to a boil. Cover and let the mandarins continue to simmer on low heat for two hours until the entire fruit is very soft and pulpy.
Preheat the oven to 350 degrees Fahrenheit.
Once the fruit has cooled, discard the water they were cooked in and remove seeds from the fruit, if any. Place the mandarins in a food processor and process into a coarse puree.
Add all of the remaining ingredients for the cake into the food processor. You can also do this in a bowl. Mix everything until well incorporated.
Spray a 9-inch cake pan with cooking spray or brush with oil. Line the bottom with parchment paper. A springform pan, is preferred, if you have one but you can use a regular cake pan.
Scrape out the batter into the cake pan and smooth the top, if necessary, with a spatula.
Place the cake in the oven and bake an hour or until a toothpick in the center comes out clean.
Place the cake pan on a rack and let it cool about 30 minutes, then carefully unmold the cake, peel out the parchment paper, and continue cooling it on the rack.