In a medium saucepan cook potatoes in enough lightly salted boiling water to cover for 20 to 25 minutes or until tender; drain. Mash with a potato masher. Let stand for 10 minutes or until cool enough to handle.
Drain any excess liquid from the salsa. Stir salsa, cheese, and sour cream into mashed potatoes; mix well. Shape mixture into eight 1/2-inch-thick patties. Place on a baking sheet. Cover and chill until ready to grill.
In a grill with an insert, arrange medium coals in a pyramid in the center of the grill. Place a griddle over coals. Cover and preheat for 10 to 15 minutes.
Grease the griddle with 1 tablespoon of the oil. Add summer squash and/or zucchini to griddle. Sprinkle with salt and pepper to taste. Cook and stir for 3 to 5 minutes or until tender. Cover and keep warm.
Grease griddle with the remaining 1 tablespoon oil. Place potato cakes onto griddle. Cover and grill for 6 to 10 minutes or until golden brown, turning once halfway through grilling. Serve with summer squash and/or zucchini.