Can a cubic meter of space at absolute zero have any object with mass inside? I ask this question because, I have seen many places where they say the average temperature of the universe is some 2 degrees K and this somehow relates to mass present within a given volume of space.
So if there is a relation between temperature and the mass present inside a volume, i want to know that if a cubic meter of space is said to be at absolute zero(no approximations) then can it be said that there is no mass bearing object inside this volume? 
Also conversely, if in this cubic volume at absolute zero, if one were to introduce say an electron or any other mass carrying particle; could it be said that the system is no longer at absolute zero?
If so can we conclude that for any system with temperature above zero kelvin, there has to be something with mass inside the system?
 A: A cubic metre void of anything cannot be described with a temperature. Spacetime itself does not have the property of temperature, so it would be incorrect to say such a void is at absolute zero.
However, it is not necessary that any volume not at absolute zero has mass. The property of temperature could be held by photons or other massless particles. For example, the photons from the Cosmic Microwave Background (CMB) - the 2.7K background you referred to - are described as having a temperature. These photons, when they are the only inhabitants of a given volume, would make the mean temperature of that volume the mean of their temperatures.
We can say, though, that any volume containing thermal particles (I mean particles describable as having a temperature and not specifically phonons or photons) is not at absolute zero. Thus sayeth the almighty Third Law of Thermodynamics.
A: As mentioned in the comment above, temperature is defined to be a measure of the average kinetic energy of the particles in a system. So with that definition, the answers to your questions should fall out naturally:


*

*If there is no mass in a volume, you could say the temperature is absolute zero. I would say it isn't defined because you cannot take the ensemble average of zero things.

*If there is a mass in the volume, it may or may not have a temperature of absolute zero. If all of the particles contained no kinetic energy, the temperature would be zero. But we can only asymptotically remove all energy which is why we can only asymptotically approach zero. 

*If any system has a temperature that can be defined, it must have some sort of mass within it. Without mass in a volume, we cannot define a temperature, zero or otherwise.
A: Temperature is a quantity that determines how heat flows into and out of a system of particles when it is placed in contact with other systems. By this definition, measuring the temperature of a system with no mass inside is nonsensical; it's not absolute zero, it's undefined.
Temperature can equivalently be defined as being proportional to the average kinetic energy of particles in a system. Quantum mechanically, if your cubic meter of space has a single particle in it, it cannot have zero kinetic energy. This is because this would imply that the magnitude of the momentum of the particle is known with 100% precision (to be zero), and by Heisenberg's uncertainty principle, this implies that the position of the particle cannot be pinned down with even the weakest precision. This means that a particle with zero kinetic energy cannot definitively be said to be in your cubic meter of space at all!
