Preheat oven to 350 degrees F (175 degrees C). Grease one 9x13 inch pan.
Place grated zucchini in a colander and set aside to drain.
Whisk together the flour, baking soda, baking powder, white sugar, brown sugar, cinnamon, cloves, nutmeg, and salt in a large bowl until well blended. Beat the eggs, applesauce, oil, and vanilla in a separate bowl until smooth. Fold in the flour mixture, then stir in the zucchini. Pour the batter into the prepared pan.
Bake until a toothpick inserted in the center comes out clean, 45 to 55 minutes. Allow to cool completely before cutting.
