With this build Hecarim can easily clear large waves of minions even if you don't get fed early which doesn't always happen with hecarim since he has more mid to late game potential he can easily level and gain a ton of gold by clearing minion waves and jungle.

Pros
Mid to late game your burst with R and Q and E plus lich banes effect will be crazy
Easy farming with W and Q
Due to easy farming kills aren't necessary
Due to easy farming very unlikely to be left behind in level and items

Cons
More mid to late game potential so somewhat weak early game
building a catalyst or ROA can fix this but takes time

Items are tricky on AP Hecarim he still neads damage cause he only has two abilities that scale with ap. having nashors tooth gives his basic attacks that extra needed magic damage and don't forget the effect of nashors also takes into account the opponenst magic resist as does lichbane so magic pen is also helpful if you wanted to you could exchange one of the items for a abyssal scepter to add a lil more power to lich bane and nashors effect
Lich bane is a huge player in this build both Q and E apply on hit effects such as lich bane's directly on cast this turns his q and e which where at first week compared to his W and R now heavy hitting burst attack