I have installed the Davdroid on my moblie (galaxy note 4, android 5). I have added my nextcloud account by two ways:
https://server.pl/nextcloud/remote.php/dav/ In this case there was no CardDav service available in Davdroid, only CalDav was available.
And second one:
https://server.pl/nextcloud/remote.php/dav/addressbooks/users/NAME/contacts/ For this time with CardDav and CalDav services comes up in Davdorid
In each of these two case I could add a new calendar and synchronize it between devices. To be clear, only the name of the a calendar has been synchonized but no content (events) has been copied.
I have tried different CalDav app and it works, so I think there is no problem with the server.
Configuration debug file
Debug file created when I have tried to sync.
Thanks for help