This is pre-Rabadon. That Zhonya's Ring is the same as Rabadon's Deathcap and Zhonya's Hourglass combined.

I don't think you need Rod of Ages if you have Mejai's and Arcangel's Staff. What happen to Rabardon's Deathcap. +155 AP and AP will attack 30% more.

i was bored so i did a match getting as much ap as possible i managed 1300ap i had archangels mejais soulstealer and 4 zhonyas rings

I dont get the Lich Bane, you dont need it at all. Killing a champion is easy enough with Veigar, you dont need the bonus damage on your basic attack passive. You would profit more from an Abyssal Scepter or Void Staff.

I changed up the item build after testing said new one. Having Lich Bane > Deathfire's. Makes your attacks deal 800-1,200 damage.