How to call a function from a class that contains a constructor without calling the constructor?

if you can't change then class, then no, you can't call a member function without instantiating an object (aka calling the constructor).

The first solution that declaring the function as static is correct, but consider that you than have no object instance on that you can perform the function.

My experience is, that a static function or such problem is only the symptom of some more hidden issues like isnt belonging into this class or the functions isnt optimal at all.

So consider redesigning this class and the function.

As suggested you have to make the method static. That's appropriate for class methods, that is methods independent on a class instance. E.g.

#include <iostream>
using namespace std;

class Point
{
private:
    int x, y;
public:
  Point()
  {
    x = 1;
    y = 2;
  }

  static Point origin()
  {
    Point p;
    p.x = p.y = 0;
    return p;
  }

  void show()
  {
    cout << "{ x = " << x << ", y = " << y << " }" << endl;
  }
};


int main()
{
  Point p;
  p.show();

  p = Point::origin();

  p.show();
}

In the above sample code, the static method origin can be invoked (and, in fact is invoked) without having a Point object reference. On the other hand, the standard (instance) method show is called having a Point object reference.
Note the origin method cannot access any Point instance member.