I noticed that some of my Google Chromecasts were on an older firmware version.

You can force a reboot and update with this command: (insert own IP address)

$ curl -X POST -H "Content-Type: application/json" -d '{"params": "ota foreground"}' http://<YOUR IP>:8008/setup/reboot -v
Note: Unnecessary use of -X or --request, POST is already inferred.
*   Trying <YOUR IP>...
* TCP_NODELAY set
* Connected to <YOUR IP> (192.168.178.113) port 8008 (#0)
> POST /setup/reboot HTTP/1.1
> Host: <YOUR IP>:8008
> User-Agent: curl/7.58.0
> Accept: */*
> Content-Type: application/json
> Content-Length: 28
> 
* upload completely sent off: 28 out of 28 bytes
< HTTP/1.1 200 OK
< Access-Control-Allow-Headers:Content-Type
< Cache-Control:no-cache
< Content-Length:0
< 
* Connection #0 to host <YOUR IP> left intact