How are you determining that the output sound is low? What are you using to measure this output?
You say sound levels are working fine with the MOXF directly?

Please check the firmware version of the MOXF again. I was not aware of version 1.3 (current version is 1.12, as far as I know)
How are you connecting the MOXF? For example, we assume you are connected to your computer via USB, but what are the Main L/R Outputs of the MOXF6 connected to?

Go to [UTILITY] > [F1] GENERAL > [SF2] OUTPUT > what are the USB1/2 and USB3/4 Gain set to, make sure they read +6dB

However moxf6 is giving very low sound as playback device, both in cubase(Cubase LE AI elements 32 Bit) and in pc/laptop(Windows 7 32 bit).

Are these not the same thing? Please explain what other application are you using other than Cubase AI — please use Cubase AI. Also what version number of Cubase AI are you running — for example, Cubase AI 10.5? Cubase AI 5? Cubase AI 6? etc.

Matching firmware Version, Driver Version, Windows Version, and Cubase version is very important. With computers you must know when to update and when not to update. You are running Windows 7, 32-bit, so it is very important to watch out for newer versions that are 64-bit only. I don’t/can’t know that this is a problem quite yet, because we need accurate answers on these versions to make a determination.

Start with your MOXF6 firmware version...
We will also need to know how you are setup to monitor the outputs of the MOXF6 (to what you have connected the MOXF6)

Let us know.

How are you determining that the output sound is low? What are you using to measure this output?
You say sound levels are working fine with the MOXF directly?

--I am able to hear all the tones/voices(including the A/D input) when monitors(KALI-LP6) are directly connected to MOXF6 L/Mono and R output.
But when the recorded audio on cubase is played it is not audible with the same level, however when i export the same as wav file it is audible on other sound device.

Please check the firmware version of the MOXF again. I was not aware of version 1.3 (current version is 1.12, as far as I know)
--my bad it is Boot: V1.01/ Firm: V1.03.0

How are you connecting the MOXF? For example, we assume you are connected to your computer via USB, but what are the Main L/R Outputs of the MOXF6 connected to?
--Yes through USB , Main L/R Outputs of the MOXF6 connected to KALI LP6 speakers.

Go to [UTILITY] > [F1] GENERAL > [SF2] OUTPUT > what are the USB1/2 and USB3/4 Gain set to, make sure they read +6dB
--Yes it is set correctly.

However moxf6 is giving very low sound as playback device, both in cubase(Cubase LE AI elements 32 Bit) and in pc/laptop(Windows 7 32 bit).
Are these not the same thing? Please explain what other application are you using other than Cubase AI — please use Cubase AI. Also what version number of Cubase AI are you running — for example, Cubase AI 10.5? Cubase AI 5? Cubase AI 6? etc.

--Cubase LE AI Elements 8...and moxf6 can also act as sound card for my pc correct(i.e i can use it for watching videos outside cubase software)?

-my bad it is Boot: V1.01/ Firm: V1.03.0

You should update your firmware (operating system) to version 1.12... the Updater is available. https://download.yamaha.com

But when the recorded audio on cubase is played it is not audible with the same level, however when i export the same as wav file it is audible on other sound device.

This is your answer... the .wav File is audible on other devices... so it follows you have some problem with how you are monitoring in Cubase. Please give us some idea on how you have Cubase setup to make the .wav File.