A large number of clathrate-like cages have been proposed as the very first hydration shell of alkanes. The cages include canonical structures commonly found in clathrate hydrates and many others, not previously reported, derived from the carbon fullerene cavities. These structures have a rich and variegated form, which can adapt to the shape and conformation of the solute. They avoid "wasting" hydrogen bonds, while minimizing the volume cage and maximizing the solute-solvent van der Waals interactions. DFT/M06-2X and MP2 ab initio calculations give comparable structural and energetic results although the latter predicts slightly larger cages for a given solute. It is shown that the van der Waals interactions are substantial and the large exoenergetic values found for isobutane and cyclopentane provide an explanation for the surprising high melting points of related hydrates at room pressure. The encaging enthalpy for various hydrocarbons is similar to the enthalpy of solution measured at a temperature just above the melting point of aqueous hydrocarbon solutions, thus indicating that water molecules should not deviate too much from the configuration with O-H bonds tangentially oriented with respect to the solute surface. The computed trend differs from the enthalpy of solution measured at room temperature, thus the very first hydration shell departs, up to a certain degree, from the clathrate-like structures.