Set up 1 station that will connect to your broadcasting software, and then setup relays on the other 5 stations that connect to the 1 station.
You should then be able to stream to all 6 stations at the same time.
Or as Roger suggested, use 1 broadcasting software and setup 6 encoders. But also, as he stated, make sure you have enough upload/upstream bandwidth to do so, otherwise there could be a lot of buffering.
That is, if you are wanting the same music and same live voice on all 6 simultaneously.