It's in your head, really. Eight vials, depending on the size needed for testing, is going to range from less than an ounce to two and a half ounces. In comparison, people who donate blood give 16 ounces.
Be well hydrated, so your pee has almost no color, starting right now. (They recommend two days before a blood donation.) Eat an ordinary meal a few hours before your donation, so it's not on an empty stomach and you didn't just eat. Do not watch the procedure but look away. Remind yourself that this amount of blood is about 1.5% of your total blood volume, or less than that, and your body can handle it easily.