Grate the zucchini with either a hand grater or a food processor with the grating blade. Place it in a mesh bag and squeeze out the water or use a strainer and press with a wooden spoon to squeeze out the water.
In a large bowl combine the cane sugar, coconut sugar, applesauce, coconut oil, and vanilla.
In a medium bowl combine the flour, baking soda, cinnamon, baking powder, salt, and nutmeg.
Add the wet ingredients to the dry ingredients and then fold in the zucchini and nuts.
Line a loaf pan with parchment paper and bake for 50-60 minutes.
Test for doneness with a toothpick to make it comes out clean.