As you may have noticed, mobafire's system does not calculate all the items passive (like the bonus AD of the atma's impaler). Here are the real stats the champion should have at lvl 18 :

Health
4326 at 18

Health Per 5 sec
101 at 18

Mana
1180 at 18

Mana Per 5 Sec
17.3 at 18

Armor
219 at 18

Magic Resist
182 at 18

Damage
241 at 18 (including hecarim's passive)

Attack Speed
1.2 at 18

Critical Chance
33 at 18

Ability Power
30 at 18

Armor Penetration
14.94 at 18

Magic Penetration
0 at 18

Movement
467

Hecarim can be played has a tanky fighter or has a pure DPS. Since all of his abilities are meant to be used to engage fights, I prefer a realy tanky build. Here's some other reason.
-Always in the fight
-Since his Q has a low AD ratio, he still deals lot of dmg in tanky mode
-DPS build is really useless, unless fed
-12 000 effective Hp, better than most tank (effective Hp = his Hp considering his armor and magic resist)
-If u combine his AD (241) and his sunfire cape (40 dmg), he deals as much dmg as the other builds

When you're fighting with hecarim with this build, you want to focus to stay near enemies.
You're primary dmg is your Q and your sheen's passive. Here's what I recommand :
-Walk near enemies, spamming your Q
-Don't "right click and wait" because each time you auto-attack, you're losing distance over your enemy
-After lvl 10, go in jungle to heal between fights
-Always use your ultimate to engage, not to escape
-You want to hit as much people as you can with your Q so stay in middle of the fight
-If you're low Hp, your W and your R is a great combo to heal on enemies

I jungle him with a standard jungle route, so you want to :
-Start at wolves, ask help of your teamates. Make sure YOU get the last hits
-Go to blue, ask a leash, smite the blue.
-Get wraith
-Kill golem. Don't use your new smite yet
-Take red, smite it
-If you have enought Hp, GANK
-If not, recall THEN gank

Here are some great spot you may want to put your Wriggle's ward.

If there's any other part of this build you want me to go over with you, put it into the comment section and I'll be happy to help.