In a large pot of boiling salted water, cook pasta according to package instructions. Drain and return to pot. Meanwhile, in a large skillet heat oil over medium. Add garlic and onion and cook until onion is translucent, 3 minutes.
Increase heat to medium-high, add beef, and cook, breaking up meat with a wooden spoon, until no longer pink, about 5 minutes. Add cumin and cook until fragrant, 1 minute. Season with salt and pepper. Add corn and zucchini and cook until zucchini is crisp-tender, 2 minutes. Add tomatoes and juice, bring to a simmer, and cook until mixture is heated through, about 3 minutes. Season to taste with salt and pepper. Divide pasta among four bowls, top with meat sauce, and sprinkle with cheese.