iPhone 13 won't install update

I have just inherited an iPhone 13 from my son. I am trying to update the software to the latest version but it doesn't work.

Phone is currently running ios 16.3 after performing a factory reset. I have looked to see if there are any updates and it gives me two options, 17.7.1 or 18.01

I tried installing 18.01 but the screen went black and pushing the power button did nothing. Managed to get the phone up and running again after what I presume is a reset of volume up, down and hold power button.

I then decided to erase the phone and start again with 17.7.1

The download took nearly an hour to complete and once it had I got a pop up asking if I wanted to install it. I clicked install and the phone powered off and turned back on again. There was no Apple logo with a status bar.

I went into see if the update had worked but it still states it is using version 16.3

I've tried installing through iTunes and a PC but the same thing happens. This is a pain as a lot of apps need version 17 to operate.

Please can anyone help on where I am going wrong or if this is a common issue as I'm totally stuck.

Thank you in advance