Hydrophobic hydration is studied with an information theory approximation, using the first two moments of the number of solvent centers in a cavity in liquid water, calculated from the density and the pair correlation function. The excess chemical potential, entropy, and heat capacity of solvation are determined for three cases: the two-dimensional MB model of water, in both the (i) NPT and (ii) NVT ensembles, and (iii) the central force CF1 model of water in the NPT ensemble. The results are compared with Monte Carlo simulations and experimental measurements from the literature. The information theory approximation, using only the first two moments, accurately determines the excess chemical potential and entropy of solvation but is unable to predict the excess heat capacity of solvation. Little difference is found between the results obtained using the uniform prior and the ideal gas prior. Molecular dynamics simulations are performed to calculate the excess chemical potential of solvation of soft-spheres as a function of solute size. These results are compared with the solvation of a hard sphere using the information theory approximation and previous molecular dynamics simulations of Lennard-Jones spheres in water. The information theory approximation is found to predict the free energy of solvation as a function of size accurately up to a cavity diameter of approximately 3.5 Angstrom.