Alex here, part of the L3D team. I checked out your link, and It looks like you got a knock-off! That's neat -- it's the first mostly-exact copy we've seen out in the wild. Our design is open-source, so that ebay seller is within his rights to make his own version, as long as he doesn't call it an L3D cube.
I'm not 100% sure that your PCB is identical to our design, so you should ask your seller for his advice/schematics/etc if your board behaves at odds with our code/advice.
For getting started, you should pull that arduino out of your circuit board -- if you have both an arduino and photon in at the same time, they'll both try to control the LEDs at the same time and they'll make a huge mess of things. You can load our official firmware onto the photon with cubedoctor and that should get you up and running. If you really want to use the arduino instead, yank the photon off your board, and check out some of the threads on the forum that give advice on using the arduino. We don't officially provide software support for arduinos, as the vast majority of our users work with the photon, but there are a bunch of our users who make and share arduino code, and their posts and work are the best place to get started.
Good luck! Please do let us know if you see any other fishy behavior with your cube -- because we didn't make it, we can't offer support for the hardware, but it sounds like your vendor is acting fishy and is palming off support onto us for a product that he made. I sympathize with your position -- you didn't sign up for this when you bought your cube, and we'll do our best to get your software working, but we literally know nothing about this guy's hardware design or production methods. Any insight you could give us into issues you have with your cube would help us figure out what to do about this guy, and how to respond to other users in your position.
Good luck, and happy cubing!