Question

How one can overload an operator<< for a nested private class like this one?

class outer {
  private:
    class nested {
       friend ostream& operator<<(ostream& os, const nested& a);
    };
  // ...
};

When trying outside of outer class compiler complains about privacy:

error: ‘class outer::nested’ is private

Answer 1

You could make the operator<< a friend of outer as well. Or you
could implement it completely inline in nested, e.g.:

class Outer
{
    class Inner
    {
        friend std::ostream& 
        operator<<( std::ostream& dest, Inner const& obj )
        {
            obj.print( dest );
            return dest;
        }
        //  ...
        //  don't forget to define print (which needn't be inline)
    };
    //  ...
};