I assume this is not a Minecraft failure, but a Hard Drive (HDD) failure.
I recommend to format your HDD and when the formatting process is complete to give it another try to install Minecraft.
Note: Formatting your Hard Drive will ERASE ALL dats that is stored on it. Please back up your files before proceeding.
If even that fails, I have only one suggestion left. Somthing in your Xbox, I think the HDD itself is failing and needs to be repaired.
You can do that by sending your Xbox to the Xbox Service Center.
Let us know if you need more information or support with requesting a repair for your Xbox Console.