Preheat oven to 350 degrees F (175 degrees C). Line a 9x13-inch baking dish with parchment paper.
Beat agave nectar, applesauce, raw sugar, eggs, sunflower oil, and vanilla extract together in a large bowl. Whisk all-purpose flour, cocoa powder, coconut flour, baking soda, and salt together in another bowl. Add flour mixture to applesauce mixture and stir until combined.
Fold zucchini and walnuts into applesauce mixture until batter is evenly-mixed. Spread batter into prepared baking dish.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, 25 to 30 minutes.