Bring a large pot of salted water to a boil and cook the broken spaghetti according to package directions until al dente (about the package time).
Drain the spaghetti and rinse under cold water until cool to stop cooking; drain well.
Place the cooled spaghetti in a large mixing bowl.
Add the sliced red onion, sliced cucumbers, chopped red, green, and yellow bell peppers, halved cherry tomatoes, sliced black olives, sweet corn, and chopped parsley to the bowl.
Pour the Italian dressing over the pasta and vegetables (use desired amount) and toss gently until everything is evenly coated.
Taste and adjust seasoning with salt and pepper if needed.
Sprinkle the grated Parmesan cheese on top and garnish with additional chopped parsley if desired, then serve or refrigerate.