Based on the description, you need to use a AV receiver. This device will split the audio and the video for your system.
In any case, I would also recommend you contacting Dell to get the correct configuration of your system with this type of device.
I have the same problem. I have my Lenovo notebook connected to external display via VGA, and Sony receiver via HDMI. It all works when I say I want to clone desktop on those two monitors, but the sound output is only stereo, there is no 6 or 8 channel, which my receiver clearly supports, because there are 7 speakers + subwoofer.
In your case, I recommend you updating the bios in your system and installing the latest audio driver from the computer manufacturer. This is because the audio controller in the computer is the responsible of outputting in different channels depending on the capability and support of it.
Due to this reason, you need to contact the computer manufacturer so they can confirm for you if the audio controller in your system supports this feature and if so, they will be able to provide the codec or software for this.