Generally most people say this build
1: Chalice
2: Boots
3: Starks
4: Aegis/Black Cleaver (if someone else got aegis)
5+6: Situational

Black cleaver adds dps and contributes even more to her supportive dps role (sivirs AS is already decently high enough so last whisper is also a bit wasted)

and for your question richochet bounces do not apply on hit effects and are magic damage so not effected by armor.

I have a mana book that gives me 25manareg at lvl 18, and 25% aspd. That way i can beat most other dps at lvl1 fights if they dont have an offensive runebook. But furthermore because I dont have to buy any mana items ever. And i can keep the richochet on the whole fight and spam boomerangs in fights and spam the shield, with discretion. I think it just helps alot more to rush starks asap and get as many towers down as early as you can before the enemy can organize agaisnt your pushes.

You can always get Bloodthirster, seeing as how Sivir can rack up them kills for the passive pretty quickly.

to OP: Nothing procs off ricochet's bounces. As to which item is better, I lean towards Last Whisper. The beautiful thing about stark's fervor is that it works for all your ricochet's bounces. It's an Area Debuff that lowers all your target's armor by 25.

Now I'm probably wrong but armor calculations go %s first, then Armor reduction, and finally armor penetration. Which means say your target has 100 armor. Well last whisper, reduces that armor to 60. Stark's then reduces that to 35. Then add in whatever armor pen runes you might have.

Now let's look at Black cleaver. After 5 attacks, you reduced their armor by 60. So we take the same 100 armor, reduce it by 60, which gives us 40, then reduce it further by 25 to 15. 20 less armor, BUT you had to attack 5 times to get that there.

Stark's plus atk speed boots alone give you around 1.5 atk speed @ lvl 18. Add in what 40% from last whisper, and your look at a .36 increase.(You get that number from sivir's base atk speed @ lvl 18, which is aorund .9. Then 40% of it is .36 and you add that on top of the 1.5 which totals out around 1.86 atk speed.

So 5 attacks with black cleaver @ 1.5 atk speed means you will reduce their armor by 60, in 3.33 seconds. In that time, You would get 6.2 attacks if you had last whisper. Barely a difference right? Black cleaver looks better right? WRONG.

If the opposing team, sees a carry with Sivir's lolcraptastic range(which is getting nerfed next patch anyways) in a fight auto attacking. They are going to squish her FAST. Do you really think you have time to ramp up 5 attacks with a black cleaver, before your focused enough where you have to retreat? Doubtful, and if you did; well the other team's ******ed and they deserve to get rolled by a Sivir.

Last whisper, allows you to take advantage of your full potential armor pen, from the get go. That's not to say, Black Cleaver is bad, it's just not worth it for Sivir. The damage on cleaver, is very nice; don't get me wrong. But for armor pen purposes, Last whisper is better in my opinion. Let Tristana or Ashe, basically somebody with a decent range on their auto attack worry about the Black Cleaver, come next patch your auto attack range is dropping to 350(your be up in the thick of it with Morgana). Last whisper allows you to shoot and scoot, much better.