Preheat oven to 300 degrees F (150 degrees C). Grease a 9x5-inch loaf pan and dust with 1 tablespoon cocoa powder.
Whisk sugar and oil together in a large bowl until smooth. Beat eggs, 1 at a time, into sugar-oil mixture, beating thoroughly before adding the next egg. Beat mashed sweet potato and vanilla extract into sugar-egg mixture until smooth.
Sift flour, 1/2 cup cocoa powder, baking soda, cinnamon, and salt together in a separate bowl. Sprinkle oats over flour mixture. Stir flour mixture, 2 to 3 tablespoons at a time, into sweet potato mixture until batter is just mixed; fold in apples and walnuts. Spread batter into the prepared loaf pan.
Bake in the preheated oven for 70 minutes. Increase temperature to 350 degrees F (175 degrees C) and bake until a toothpick inserted in the center comes out nearly clean, 20 to 30 minutes more.