Why is logP quite a bit lower in cyclohexane than in hexane?
Think of the hole in the water that the molecules occupies as a bubble. The bigger the bubble the greater the area over which surface tension is acting. 

The highest volume to surface ratio is for a sphere. So hexane is like a rod and cyclohexane is like hexagonal pyramid. Guess which has a higher volume to surface ratio?



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Not that it is exactly the same, but look at the densities of the liquids. The cyclohexane molecule occupies a small volume in the liquid as compared to hexane, hence it is denser, even though it has 2 hydrogen atoms less per molecule. 

Now water has 18 ml/mole so we can figure out roughly how many water molecules are displaced by a molecule of each hydrocarbon.

                                                     # water
                                                     molecules
             density         molecular mass  ml/mole displaced
Cyclohexane  0.7781 g/mL     84.16 g/mol     108.2    6.0
Hexane       0.6548 g/mL     86.18 g/mol     131.6    7.3