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 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.
I think your mileage will vary depending on your own situation. Your other home devices, your location, how well the power supply in your gear deals with the particular combination of noise, and voltages you have.

My favorite, cost effective solutions for this are the Furman with SMP and LiFT.

If you can afford power regenerators like PS Audio, even better.