Fill a large pot with water and bring to a boil. Cook the spaghetti according to the package directions until al dente. Drain and rinse under cold water to stop the cooking process, then set aside.
In a large mixing bowl, whisk together the olive oil, lemon juice, agave syrup, and Italian seasoning until well combined. Season generously with salt and pepper.
Add the halved cherry tomatoes, sliced cucumbers, chopped red onion, and both types of olives into the bowl with the dressing. Mix well to ensure the vegetables are coated, and let them sit for about 5 minutes to marinate.
Once the pasta has cooled, add it to the bowl along with the crumbled feta cheese. Toss everything gently but thoroughly so that the pasta and veggies are well integrated.
Taste and adjust seasoning with additional salt, pepper, or lemon juice if desired. Serve immediately or refrigerate for 30 minutes for enhanced flavors.