What is the reason octane (C8H18) is a liquid at room temperature while methane (CH4) is a gas at the same temperature?

We are talking about the difference in the physical state of octane versus methane at room temperature.  Methane is a very small molecule with a molecular weight of 16 g/mol.  It exists as a gas at standard temperature and pressure.  Octane is a much larger molecule with a molecular weight of 114 g/mol.  It exists as a liquid at standard temperature and pressure.  

All gasses at room temperature and atmospheric pressure are comprised of small molecular weight molecules.  The smaller a molecule, the more degrees of freedom of movement the individual atoms and bonds have.  The increased movement of these smaller molecules allows them to have more space between the individual molecules.  This increased molecular motion and space between molecules is one of the defining characteristics of a gas versus a liquid (or solid).  The larger octane molecules have less degrees of freedom and less molecular motion so they are able to be closer together, thus existing as a liquid instead of a gas.