Cant install games of Xbox app in an external hard drive

if you are trying to install them in an external hard drive for the xbox 360 then that might be the problem, if it is possible, try to install them in the internal hard drive of the console, once you do that try to start the apps and to check the external
hard drive is not damaged try to start a game from there

You may have filled your internal hard drive, and now need to tell the games and apps to install to the external hard drive.

I know there are a lot of posts but let me re-summarize.

Hard drive was working with everything.

Xbox updated.

External Hard Drive allows Apps to install no issue, but games will not install or be moved to the External Hard Drive.

Games that were on the external drive still work but are no longer able to update and as such error out when attempting to play.

Given hardware did not change and is still in working order as evidenced by being read and installing Apps (small sized files compared to games), the only thing that changed was software (the update).

Some users report certain external hard drive enclosures work still ($7.99 on Amazon) but previous ones stopped. This tells me there is a driver incompatibility or a soft block on certain external device enclosures.

Yes, I have an external hard drive connected to my Xbox, and the game appears to be installed on the external hard drive.

I'm gonna be more specific: the game doesn't accept installation on external storage. Whether it's flash drive or external hard drive, the game isn't meant to install on external storage connected through USB just like Need for Speed Rivals on Xbox 360.
You need to install it on an internal hard drive (media hard drive). The link I provided to you aren't external hard drives; they're internal hard drives for the Xbox 360:

http://www.xbox.com/en-US/xbox-360/accessories/harddrives