Preheat the oven to 350 degrees. Spray a loaf pan with cooking spray. Set aside.
In a medium bowl combine the flour, baking soda, baking powder, and cinnamon. Set aside.
In a large bowl combine the egg, applesauce, oil, vanilla, and sugars. Mix well.
Stir the dry ingredients into the wet ingredients and mix until just combined.
Gently stir in the squash and apple until they are mixed in.
Pour the mixture into the prepared loaf pan and bake for 55-65 minutes or until the top is golden brown and a toothpick inserted into the center comes out clean.
Remove from oven and cool for 15 minutes on a wire rack before removing from pan and cooling completely.