Why cannot update my system?

Error 504 means the app couldn't be downloaded due to an erorr, or the gateway timed out. So if it is a HTTP error, it means the server in between you and Google timed out hence the problem!

I am not sure if you are on Wi-Fi or a cellular network, but you can try this anyway I guess! Go to Settings and find Airplane mode, you may be able to get to this by sliding in from the top of your screen as well. Turn Airplane mode on and wait a ten seconds or so, and then turn it back off. Check your Wi-Fi or cellular connection and wait for it to reconnect. Make sure you are using a good internet connection as well.

You should also check your storage space and ensure you have enough storage!

Try updating the application again. If you still get the error, go to the next step!

1. Clear Data - Go into your settings and then go to Application Manager or Apps (it may be listed as something else, try and find where it lists all of your apps). Find Google Play, click "Force Stop" and click the "Clear Data" button.
2. Once you have cleared the data, clear the cache. It will be close by the Clear Data button.
3. Next, go back where it lists all of the apps and find Google Service Framework. Clear the cache of that app as well and data.

This is the last method and it involves a little bit more.

1. Remove Gmail Account - You will need to remove your Gmail account. You can accomplish this by going into Settings >> Accounts & Sync. Find the gmail account you wish and delete the account.
2. Reboot your phone.
3. Go back into settings and Accounts & Sync. Add the gmail account again.

Go back into Google Play and try to update the apps.

Hopefully this works for you!