In a mixer or blender, blend eggs, yolks, sweetened condensed milk, whole milk, vanilla and cream cheese and beat 10 minutes. In a heavy-bottomed saucepan, melt sugar over medium heat until caramelized. When sugar is melted and golden brown, add water. Stir to combine. Pour a little of the caramel into each of dozen individual, ovenproof flan dishes. Divide milk mixture evenly among dishes. Set dishes in a larger baking dish;fill baking dish with water to come up halfway on flan dishes. Bake uncovered at 200 degrees one hour.