Using a sieve, sift sugar, paprika, salt, cocoa, cayenne, and cumin together into a small bowl. Stir to combine.
Working with one rack at a time, lay a long piece of plastic wrap on the counter and place ribs on top. Sprinkle one-quarter of spice mixture evenly over both sides ribs, then lightly rub mixture in to coat completely. Wrap in plastic and refrigerate at least 20 minutes (or up to 2 hours for maximum flavor).
Preheat oven to 350°F, with racks in upper and lower thirds. Line 2 rimmed baking sheets with foil, and set a wire rack on top of each. Transfer 2 racks of ribs, unwrapped, to each wire rack, meat side up.
Cook ribs, switching position of baking sheets about halfway through, until meat pulls away easily from the bones, 1 ½ to 2 hours.
Remove racks from oven and increase temperature to 425°F. Brush both sides of ribs with 2 cups of barbecue sauce.
Return ribs to oven and bake until sauce is slightly caramelized, about 15 minutes. Let stand 5 minutes; serve with more barbecue sauce.
