Why do I need a special cable?
You don’t!
the Beosystem 3 has more powerlink sockets and if I use for every Beolab an extra socket (one for left, the other one for right…..) this would not work?
Correct, you’re right this would work.
We have this discussed here too …
https://archivedforum2.beoworld.org/forums/p/37113/280720.aspx#280720
Interesting, but….
there is a difference. If you connect them to a Beosound the PL will always have the right and left channel.
if you PL connect the speaker to a BV7 and instruct to play for example “front right” to this PL connection then it only will play this channel.
That said, with the quoted post in mind, you should not chain the speakers but feed/connect them separately.