Now veigar is a hardcore scaling champ. People always try to get the most AP on him by going full glass cannon. But that isnt the most efficient build. By only getting, morellonomicon, deathcap,and void staff you easily reach 1000 AP around 25-30 mins if you stack well. If you were to add on a ludens echo or liandrys your AP wouldnt go up by much (trust me ive done it before). Since your main source of AP is from deathcap synergizing with your passive. With 2 item spots left open you should start building tanky. Banshee veil and randuin will make you a 1000 AP tank. Veigar isnt mobile so enemies can jump on you easily. With 2 tank items they wont even be able to kill you before you blow them up.

-Rush lost chapter and then a tank item and continue on with normal build if youre getting stomped in lane
-Stomping enemy mid laner, get morello deathcap and void then go tank.
-Dead even then go morello, deathcap, first tank item, void, second tank item.

DONT FORGET LUCIDITY BOOTS.

This about wraps up my guide, just remember when youre about to build full glass cannon, is that you cant do the damage if you get bursted ;).