That's about 6,220 metric tonnes, or more than 6 metric megatonnes.
Correction, 6 metric Kilotonnes (Kilo is *10^3 and Mega is *10^6)
It's not even about weight, although that's valid.
We aren't talking about Weight, we are talking about Mass. Mass is how much stuff there is and Weight is just the force exerted on that mass by a gravitational field.
As for working out the density, it is simply mass/volume. If we know the mass of 1 cubic meter of stone, then we know the density (which, for a meter cube is equal to the mass in this case).
Putting the numbers in, 64*2700 = 172,800 kg/m^3
As for whether it would be a black hole, we need the formula for the Schwarzschild radius, which gives the radius of the sphere where, if all of the mass was compressed into this sphere, the escape velocity would be greater than the speed of light.
r = (2GM)/(c^2) G = 6.67*10^-11 (or the gravitational constant) and c = speed of light in m/s, or 3*10^8
Putting in the nymbers, r = (2*[6.67*10^-11]*172800)/[9*10^16]
That gives a radius of 2.56^-22
As for the centres of stars, it would completely depend on the star but most have a core of iron, so for the most part it won't be, if it is a new star then it would most likely be a core of hydrogen/helium, so it would be denser than them.
I think I've read somewhere that weight increases with density. Which is why black holes have such immense amounts of gravitational pull.
Only because density just tells you how much stuff there is in a certain volume, if you have a higher density, you have more stuff, so you have an increased mass (and by relation, increased weight).