Preheat oven to 350°F. Prepare all 3 packages of cornbread as directed. Bake cornbread in greased 10-inch cast iron skillet. Meanwhile, boil squash, zucchini, bell pepper and onion in chicken broth until vegetables are very tender. Drain, reserving all liquid in separate bowl.
When cornbread is done, set out to cool. When cooled, crumble in large ovenproof bowl, such as a Pyrex bowl. Add drained vegetable mixture, the 5 whipped eggs, shredded cheddar cheese, enough of the reserved vegetable broth just to moisten cornbread and vegetable mixture, careful not to make it too moist.
Put in preheated oven until golden brown and edges are beginning to get dark, approximately 1 hour 15 minutes (cooking times may vary).