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 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
Some here make categorical statements implying that what they say or have experienced is always how it is for everybody. Not so! Example: Power amplifiers should never be plugged into a conditioner/regenerator because it will restrict dynamic response. Sometimes yes, sometimes no. A lot depends upon the amplifier’s design. In my particular case each transistor in my amp has a large value, quality capacitor right next to it. All those caps in aggregate store a lot of power to deliver the dynamics when they are there to be reproduced. A further advantage I have is running two powered subwoofers so the main amp is not called upon to power the deep bass notes.

I don’t doubt that there are amps who do not play well with power conditioning/regeneration, but some do. Each one of us has to know our components and how our systems respond under varying conditions.