New power cord needed for speaker with powered subwoofer?

There is no benefit in substituting an "audiophile approved" power cord to your sub.

I use two PS Audio P10 regenerators for my system, and this past year I upgraded my system's sound purely with changes in aftermarket power cords.  Yep, even with a really good regenerator between the wall and the equipment I found the improvement significant enough to plunk down my dollars, and this was with a significant home trial period allowed.  Just the change in power cords seem to bring my system's sound significantly closer to the sound of live music, with better dynamics and truer tonal quality.  Just my experience, in my system, to my tastes, YMMV, etc.

I'm an engineer, and I used to believe on principle that power cords could not make a difference (assuming adequate current capability).  But actual listening trials converted me from a skeptic on "theory" into a believer in practice.  I'm just saying "Give it a try".  With return privileges is best, then what do you have to lose?

There are many companies that will give you an audition period for their power cords and all you have to do is pay for return shipping.
Try it yourself and let your ears be the judge, as mentioned by jbrrp1.

I had changed to a higher quality power cord in one of my source components and one of the first things I noticed was a change in the mid to upper bass range. Trying different cords made the sound range from muddy to much improved clarity. Especially in the upper bass range.

amg56"A fancy power cable isn't going to enhance what comes out of the wall. In fact it may amplify the bad stuff."

A power cord is a "passive" device and is unable and incapable of amplifying anything this is introductory, basic, and fundamental physics otherwise you would have perpetual motion!