https://en.wikipedia.org/wiki/Solar_System suggests 40AU is a reasonable radius (call it 6 billion km). Which gives a spherical volume of 9.05x10^38 m^3 giving you one address per 4.16x10^10 km^3.
You could consider it a disc that just encapsulates the sun - then the volume is 1.57x10^35 m^3 and your address gets you a mere 8.5x10^6 km^3.
You could consider it a disc that just encapsulates the sun - then the volume is 1.57x10^35 m^3 and your address gets you a mere 8.5x10^6 km^3.