1.354e14 kg assuming the Death Star has a radius of 160 km. However there's conflicting information about the diameter of the Death Star (some say 120 km, others 160 km) and that's the diameter and not the radius.

So the Death Star would be considerably lighter than your friend's calculation.

My calculations give 3.385e13 kg assuming a radius of 80 km which yields a density of 1.578e-2 kg/m3 or 15.78 g/m3 which is way, way low. In fact it's much lower than the density of air.

Three possibilities: I made a mistake in my calculation, Google's gravity value for the Death Star is incorrect, we shouldn't expect consistency from a story George Lucas made up almost 40 years ago.