Try something as following in cron:
DISPLAY=:0 DBUS_SESSION_BUS_ADDRESS=unix:path=/run/user/1000/bus /usr/bin/notify-send "This is a test."
Where, 1000 is your user id and it can be located with id command:
id -u
For sudo try (run it as foo user with id 2000):
/usr/bin/sudo -u foo DISPLAY=:0 DBUS_SESSION_BUS_ADDRESS=unix:path=/run/user/2000/bus /usr/bin/notify-send 'Hello world!' 'I am running and doing something for you.'