The roles of hydrogen bonding and the hard core of water on hydrophobic hydration are clarified using Monte Carlo simulation and the test particle method to compare the cavity formation in water with that in a Lennard-Jones (LJ) fluid with the same molecular size and density. Similarities and differences in the cavity formation in the two fluids are examined in terms of the free energy, the energy change, and the change in the coordination number upon cavity formation. The free energy of cavity formation at a given density and the decrease in the coordination number around cavities in water are similar to those in the LJ fluid. These similarities are due to geometrical restriction of the hard core of molecules. The effect of the hydrogen bonding of water can be seen in the coordination-number dependence of the average energy of one molecule, regardless of whether water is in bulk or in the hydration shell. The temperature dependence of the correlation between the coordination number and energy can explain both the temperature dependence of hydrophobic enthalpy in the thermodynamic level and that of molecular energy changes near cavities in the molecular level. We conclude that combining the water-specific coordination-number dependence of energy (the hydrogen-bonding effect) with the decreased coordination number around hydrophobic groups (the hard-core effect) explains the special characteristics of hydrophobic hydration, such as iceberg formation, the entropy decrease at room temperature, and the large positive heat capacity change.