Make an external HDD work with Xbox 360?

I, like many people, got the new Xbox for Christmas. However, my mom failed to notice that it was the 4GB model, rather than the awesome 250GB. When I realized this, I immediately went online and looked for a 250GB Xbox S Hard Drive, and found that they're $130($0.52/GB)! Well I knew that the Xbox can use flashdrives for storage, etc. so it should treat an external hard drive just like a big flashdrive, right? So I went to BestBuy and bought a 500GB external hard drive for $60 ($0.12/GB- 4.3x cheaper!). Upon plugging this into my Xbox, and going through the configuration process, I see that my Xbox is only picking it up as 16GB. "Are you kidding me? There's a lot more than 16GB on that thing!" I went online, and did some Googling, and YouTubing. All I could find was formatting the drive, and even then only being able to transfer movies, music, etc from you computer. I read multiple times that you couldn't put games or profiles on it(I wanted to do this, so I could transfer everything from my old original Xbox 360 HDD, and then sell it). Could somebody please tell me a way to make an external hard drive work with Xbox 360? I'd rather not format anything, but I will if I must. Thank you!

afung5 years ago
He mumbles a lot, but I think it should work since it's only a month ago. Not sure if the recent update has ruined anything. But Good Luck!