Preheat oven to 350 degrees F (175 degrees C). Grease and flour an 8-inch baking dish or cake pan.
Whirl the pulp in a blender until smooth. Blend together the persimmon pulp and baking soda in a small bowl.
In a large bowl, cream together the butter and sugar until fluffy. Add the puree to the creamed mixture. Sift together the flour, baking powder, salt, cinnamon, nutmeg and cloves; gradually blend the flour mixture into the persimmon mixture. Stir in nuts and citrus zests; batter will be stiff. Spoon into prepared cake pan.
Bake in preheated oven until a toothpick inserted in the center comes out clean, 30 to 40 minutes. Cool the cake in the pan for 10 minutes, and turn out on a rack to continue cooling an additional 20 or 30 minutes before serving. Sprinkle with confectioners' sugar and serve warm.
