Puree zucchini/summer squash/beets and apple sauce in blender until smooth. Set aside.
Combine sugar, oil, yogurt, and eggs in a large mixing bowl. Beat with electric mixer 2 minutes.
Add cocoa and vanilla to pureed mixture; beat another 90 seconds. Add this mixture to zucchini/summer squash/beets and apple sauce.
Combine flours, baking soda, salt, and cinnamon. Gradually sift into the prepared batter, mixing it in with a spoon but stirring only until blended.
Stir in chocolate chips and nuts. Pour into greased 9x13-inch baking pan. Bake in preheated oven at 350°F until knife inserted in center comes out clean, 40-50 minutes. To bake in a bundt pan, pour half of batter into the greased pan, sprinkle chocolate chips evenly on top, then add remaining batter.