You will will need some sort of switch box to connect 1 set of speakers to 3 PCs. You can't do it just with cables - in effect you would be wiring together the outputs of the 3 PCs, and they will be VERY VERY VERY unhappy about that, even when only 1 PC is turned on. Most electronic devices will self-destruct when fed a high-level signal into their output, and your sound cards are no exception.
A good general wiring rule is that it's OK to split outputs (i.e., 1 PC to 3 pairs of speakers) but never split inputs (i.e., 3 PCs to 1 pair of speeakers).