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You make the basic mistake of taking Dark Matter at level 4. This should not be taken until at earliest, level 8.
Greatest mistake is the lack of CDR after Deathfire Grasp. For a burst AP mage, the most important stats are AP, CDR and Magic Penetration (mana as well, if necessary). Your third build doesn't even have any CDR.
You always rush the wrong items in the wrong order. The closest to being accurate is build number two, but even then you rush Void Staff over Zhonya's Hourglass when Veigar is notoriously squishy.
Your glyphs are wrong. Either take scaling AP or flat magic resist.