The Maximum Stats Possible with items alone
Now before you look at the builds, i considered and left out a lot of things which i will list
-All tested and calculated as if champs had 0 mana, movement speed, attack speed, mana regen, attack damage, and so forth
-no lifelines or actives. You could be walking down lane, be in the jungle, or under fountain and these would be the same (but not in combat)
-no infinite stats (veigar, thresh, sion, etc)
-weird thing for lifesteal, omnivamp on hextech gunblade, or things like it (death's dance, elixir of wrath) don't count as "life steal" so in game it says 56% lifesteal
-also 3 
means 3 ravenous hydras and one elixir of wrath
I believe that covers all of it.
MANA
6
or 6
= 6000
AP WITH MANA
4
= 1067.85 (less than AP without mana because as i said calculated as if champs have 0 mana
AP WITHOUT MANA
5 = 1073.25
ATTACK DAMAGE
6
=480
or
6
=480
or
6
=480
or
6 =480
LIFE STEAL
3 = 101%
ATTACK SPEED
6 
= +300% attack speed (total 400% attack speed)
ARMOR
6 
= 600
MAGIC RESIST
6 
= 420 (LOL)
ARMOR PENETRATION
3 
= 60 + 45%
MAGIC PENETRATION
4 
= 75 + 35%
HEALTH
5 
= 5405
HEALTH REGEN
5 = 1200% + 25% total
Mana Regen
6 
MOVEMENT SPEED
5 
= 115 + 50% base movement speed
I'm pretty sure that's it, if i missed anything, sue me. The only reason i did this is because no one else would and i was really bored. Also I know this should go on the gameplay boards, but there things just get downvoted and no one would end up seeing it