if i'm reading this right..
you have RCA on the ends of ur altec lansing. Easiest way is to get an Audio Receiver or Amp and plug the RCAs into there and plug ur gamecube into the Audio Receiver.
Otherwise... if ur speakers got 2 RCAs (1 white, 1 red) , then simply go to your nearest radio shack and buy those male to male (or female to female - i forgot which one is male/female

) connectors and stick them between the cables of ur GC and ur speaker.