What is the net amount of energy released when one mole of is produced?

The net amount of energy produced can be obtained from a table of enthalpy change of formation, available online.

The enthalpy change of formation indicate how much energy the 1 mole of the product (H2O) has relative to the elemental reactants (H2 and O2).  In other words, the "lost" energy equals the heat/energy released. 

For water (H2O), this value is -285.8 if the final product is a liquid under standard conditions, and -241.82 if the product is in gas form which contains some energy that could be further released.  This means that if the final product (H2O) is in liquid form, energy released is 285.8 kJ/mol.

Since water is in liquid form under standard conditions, the first value (285.8 kJ/mol) is generally appropriate.