HDMI output issue with Raspberry Pi 3

You need to edit /boot/config.txt file in order to enable HDMI forcefully ie even if no display is connected.
  hdmi_force_hotplug=1
  hdmi_drive=2
  hdmi_group=2
  hdmi_mode=81 

the second entry 'hdmi_drive=2' force HDMI mode rather than DVI, this makes audio works in DMT (computer monitor).

complete file config.txt

The 64 MB partition of the SD-card is mounted as /boot when OS is booted and running.

for video mode settings:
http://elinux.org/RPiconfig#Which_values_are_valid_for_my_monitor.3F

hdmi_drive=1 Normal DVI mode (No sound)
hdmi_drive=2 Normal HDMI mode (Sound will be sent if supported and enabled)

hdmi_group=1 CEA # TV

hdmi_group=2 DMT # Computer monitor
 

hdmi_mode=81 1366x768 60 Hz