Can I use xbox 360 cover on a fake game?

Completely fake. Christmas poster, 2 copy's of COD why?, Black box covering something. The only time you will see a deal like this from game is where you will have to trade your Xbox 360 slim with 2 games to get it at this price.

Means no more covering up fake gamerscores

where did you get the drive if not from a store but online then chances are you got a fake hard drive. fake drives while can be used on the 360 they are missing the emulation software partition to allow the old games to play.

I feel like this is a fake report, IGN would have had this covered this big time.

This isn't getting off topic. It should make no difference for OP, whether or not his drives are genuine or not.

The Xbox 360 HDD is a regular 2.5 inch HDD. There's nothing special about it--aside from the HDD running custom firmware, and a special proprietary file system that only the Xbox 360 can recognize. It has some security sectors, along with two partitions.
One is for backward compatibility emulation profiles, its associated information, and the other is for 360 related save files, videos, dashboard data, and so on. If your drive is recognized by the 360, it has the 360 partition on it. Hence, all 360 games will
recognize it as a 360 drive. The reason that B/C titles don't work is because a lot of these fake drives do not have the first partition on it, which is why when booting up your game, it fails. The other issue with fake drives is their build quality. Drives
are mechanical. They're going to fail. Fake drives don't pass QA, are cheaply built, and fail within a few months of purchase at best. There is no technical way, at least on an Xbox 360, to check whether or not drives are genuine or not. If that was possible,
you can rest assured that Microsoft would update the dashboard to reject any fake drives. Unfortunately, this is just not an option.

This game, as far as I can find, doesn't require any HDD to play. However, OP can check this by looking on the back game cover. If it says "Hard Drive Required" near the bottom, on the back, where it tells you how much storage you'll need for a save file,
how many players the game supports and so on, then you don't need an HDD. Considering he said installation fails, there must be another issue preventing it from completing. Games that require HDDs refuse to accept anything other than an HDD anyway.