Crumble ground beef into a large pot. Add diced tomatoes, tomato sauce, carrots, onion, sugar, vinegar, bouillon cubes, salt, and pepper. Pour in 1 quart of water and bring to a boil. Stir to break up beef while heating. Once the soup comes to a boil, reduce the heat to low, cover, and simmer for 30 minutes.

Pour in remaining water and return to a slow boil. Add cabbage and garlic. Simmer until cabbage is tender, about 25 minutes. Ladle into soup bowls to serve.