Power conditioner and high end power cord

I am setting up my first system and need to understand if you have a good power conditioner (EQUI=CORE 1800) do you still need these high end AC power cables. The cable I got with the conditioner 6 feet looks very high end not sure how it's made. I have all my components (two -MC601mono blocks, C2600, MD550, MT10, two JL Audio E112 sub, and JL Audio CR-1) going into the EQUI=CORE 1800. If you switch all the components to a higher end AC cables is the sound any better. Or do you need just a high end power cord from the wall to the conditioner and use the cables to the components that they came with. Any help would be appreciated. 

I would imagine it depends on the incoming power in your area and the power supplies of your equipment.  The power supply in my TRL DUDE is about as heavy duty as any amp, yet the sound improved very noticeably when I added a Core Power Tech Equi=Core150 PC and ran it directly to the Maestro wall outlet.  This is even though I was using at least a mid level power cord prior.  Surprised me how much difference it made on that one.  I have 3 dedicated 20 amp runs to the circuit box but it's not a separate panel from the rest of the house FYI.
I don't believe anyone would hear  "SIGNIFICANTLY" better sound reproduced from any "one" tweak in their audio system.  I do, however, receive more information through my speakers having added the TORUS RM-20 power conditioner, (two years ago) whether the source is from my TT or CD transport.  Simply more information.  One thing that should be determined in a forum such as this one is:  Does a tweak give you "better" sound or just "different" sound. A difference in the information you hear can be quantified, but is that difference actually "better" ?  I just added an Audioquest NRG-Z3 power cord from the TORUS to my amplifier.  This was added as a request from a retail audio boutique owner I've know for many years.  I use good quality cable for interconnects and I terminate these cables myself so I'm not one to purchase expensive cabling. HOWEVER... this Audioquest AC cable created a very discernable change in what I was hearing through my speakers and I'm still (after a week) not sure if the change is better than I was hearing before, but it's certainly different and I don't know why.  To be truthful, I didn't want to hear a difference.  I wanted to return this cable and get the refund promised if I wasn't convinced that it improved the sound. Now it's a conundrum ..
I thank you all for your input it was helpful and looks like I need to do some comparison. 
Someone  asked who I bought the core-1800 from it was a small company in Colorado I think his name was Mark. I bought it brand new it took a month plus to get it seems like a small family operations they where very good people to deal with because it to longer to make and ship they took $500 off the unit and I paid $1,200. 
You are venturing into shark infested waters. 
Mark sold the company recently and many buyers (including myself) are owed merchandise.
I own 2 Equi-core 1800's and they work as they should, thankfully.

If you want to connect everything ina protected environment, just buy a big Torus. 
I connected my’tubed mono amps, pre and sources to my AVR16 with great benefit in sound quality. 
It came after the all passive Lessloss, Acoustic Revive and 2 Bybee conditionner.
Just be careful to over dimension a bit the transfo for the system. 
Better SQ and better protection. Sound the same any hour of the day.
Just my 2 cents