Connecting Behringer UB502 to FCA202

Greetings

I have a question about connecting a mixer to a Firewire interface.

I have a Behringer Eurorack UB502 MIxer, and until now I have been connecting it to my computer from the Main Out using a cable that connects with the mixer using two 1/4" jack plugs (one Left and one Right) and at the other end becomes one 1/8" jack plug that goes straight into my computer. But I have just got a Behringer FCA202 Firewire interface, which connects to my Mac by Firewire, and I want to connect the UB502 to that. My question is, do I need a new cable - one that has a Left and a Right jack at either end. On the back of the FCA202, there are two inputs sockets, marked 1/L and 2/R. If I use my current cable, I can connect to the 2/R socket using an adaptor (because the plug is 1/8") and I get a signal. Is there any point in my going out and buying a cable with two 1/4" plugs so I could plug into the two sockets?

I hope this makes sense, and I appreciate your taking the time to read it. Any suggestions would be welcome.

Thanks in advance