Combine ham hocks and 6 cups water in a stockpot; bring to a boil. Reduce heat and simmer 15 to 30 minutes. Stir in ham bouillon cubes, sugar, brine and pepper.
Transfer ham hocks and greens to a 5-quart slow cooker; pour cooking liquid over top. Cover and cook on low setting 8 hours or until greens are tender but not mushy, adding more water as necessary to keep crock at least half full of liquid.
Remove ham hocks, dice meat and return to slow cooker. Serve over rice, if desired.