Sounds like electrical noise on the board/chipset itself. Probably not much you can do other than buying higher impedance headphones (and darker ones as more silibant bright models make that more obvious) that might mask the noise a bit.
Newer Nokias improved that a lot... on my E72 I get no whitenoise and when the music pauses you get full, dark flat silence, even with background processing and very low impedance headphones.
You might have to dump the E63 if you're looking for a more audiophile-tasting sound.