To answer the original question: based on my experience, and assuming the proper gauge for each application, *some* competently constructed power cables can affect the sound by:
a) lowering noise (line, RFI, etc); and
b) reducing impedance from the wall to the power supply vs other cables (thus improving impulse response, where required).
The audible effects can vary based on the resolution of the connecting component and the quality of its power supply, as well as affect the sound of components not necessarily directly connected with said cords (because said competently constructed cords radiate less noise, especially at the basic frequency of 50-60Hz; components that benefit so indirectly are usually phono stages)
a) lowering noise (line, RFI, etc); and
b) reducing impedance from the wall to the power supply vs other cables (thus improving impulse response, where required).
The audible effects can vary based on the resolution of the connecting component and the quality of its power supply, as well as affect the sound of components not necessarily directly connected with said cords (because said competently constructed cords radiate less noise, especially at the basic frequency of 50-60Hz; components that benefit so indirectly are usually phono stages)