Place cheese cubes in small resealable freezer plastic bag; seal bag and freeze at least 1 hour.
Heat oven to 375°F. Line 15x10x1-inch pan with foil; spray foil with cooking spray. In large bowl, mix bread crumbs and 3 tablespoons of the pasta sauce. Stir in beef, onion, salt, oregano and egg. Shape mixture into 18 (2-inch) balls. Press 1 cheese cube into center of each ball, sealing it inside. Gently place in pan. Bake 10 minutes.
Meanwhile, pour remaining pasta sauce into 5-quart Dutch oven. Cover; heat to simmering over medium-high heat, stirring frequently. Gently stir in meatballs; reduce heat to medium-low. Cover; simmer about 10 minutes, stirring occasionally, until meatballs are thoroughly cooked and no longer pink in center.
Meanwhile, cook and drain spaghetti as directed on package; keep warm.
Serve meatballs and sauce over spaghetti. Serve with Parmesan cheese.