I downloaded Fedora 27 for Virtualbox (.box file) from this webpage https://app.vagrantup.com/fedora/boxes/27-atomic-host, but cannot find the default username and password. I tried username fedora with password fedora, passw0rd, and tried without a password but all failed. Someone advise to set the default password myself but cannot find how to do that.
Default username and password for Vagrant boxes is
root password is also
vagrant) but you shouldn't need it,
vagrant up inserts SSH key to the machine and you should use
vagrant ssh to login to it without password.
Also Fedora 27 is no longer supported, its support ended in 2018, you should use latest version (33).