How to connect a double ended red/white cable to my iPhone?

My gym has a double ended red/white cable attached to the stereo in the studio which you can't take out, Is there a cable to covert this to an auxiliary cable so I can attach my iPhone?

That depends on what connectors are on the end of the cable in the gym. There are various cables for attaching an iPhone to audio systems. Do an image search and you should find something that matches.