hi fi newbie - probably biggest issue is your MP3 player is feeding a (quiet) headphone volume level to the amp (thru the 3.5mm stereo mini jack), when what you want is a (loud) line out signal.
Thus your MP3 player would sound much quieter than a CD player (or DVD player, or Freeview box connected with RCA line out cables).
For Sony MP3 players, such as the NWZ A818B, the sony docking unit is required to get the proper line out volume instead of the headphone volume.
Changing the cable is probably not going to help - although with Apple iPod the right cable bypasses the headphone circuitry and gives a true line out signal.
Other issues to consider are quality of your RIP's (MP3, WMA etc, -- the bit rate 128kb, 256kb etc, -- and the ripping software used LAME, itunes or Windows Media Player etc).
Personally for generall listening my MP3 player (Sony 818) sounds very good through my AudioLab 8000s amp and Monitor Audio RS1 speakers. But not as good as my Marantz CD63KI CD player.
I'm planning to get a dock when they come in to fix the volume, and latter a DACmagic to go straight from PC to amp.
I'm also planning to rerip my stuff to FLAC using dbPowerAmp for secure CD ripping, rather than my current Windows Media Player and 256kb MP3.