(a) Earth's mass is about 6 * 10^24 kg, and 30 feet is about 10 meters.
So the density of this cube would be about

  D = M/V = (6 * 10^24 kg) / (10 m)^3 = 6 * 10^21 kg/m^3.

Liquid water is 1000 kg/m^3, so this cube would be 6 * 10^18 times denser.

A proton is about 10^(-15) m in diameter, and has a mass of about
10^(-27) kg.  So a proton's approximate density is

  D = M/V = (10^(-27)) / (10^(-15))^3 = 10^18 kg/m^3 

and this super-compressed cube will be about 6000 times more dense.


(b) The rest mass energy of a proton is

  E = mc^2 = (1.673 * 10^-27 kg) * (3 * 10^8 m/s)^2 = 1.5 * 10^-10 J

Since particle energies tend to be quoted using electron volts, you may need
to convert the above to make comparison easier:

  1.5 * 10^-10 J = (1.5 * 10^-10)/(1.6 * 10^-19 J/ev) = 9.4 * 10^8 ev

That is, the rest mass energy of a proton is a little less than a billion ev.


(c) The superdense matter is about 6000 times denser than a proton.  Since
matter and energy are interchangeable via E = mc^2, the energy density of the
matter is also 6000 times greater than a proton.  Thus, a proton-sized piece
of this matter would contain

 E = 6000 * (9.4 * 10^8 ev/proton) = 5.6 * 10^12 electron volts, or
   = 6000 * (1.5 * 10^-10 J)       = 9.0 * 10^(-7) Joule.

(d) If the energy output of an atomic explosion is 10^11 J and is produced in a
volume of 1 m^3, then the energy density is 10^11 J/m^3.

As mentioned in Part (a) above, a proton's diameter is about 10^(-15) m.
So the energy density of the superdense material is about

   9.0 * 10^(-7) J
  ---------------- = 9.0 * 10^38 J/m^3.
  ( 10^(-15) m )^3

This energy density is 9,000,000,000,000,000,000,000,000,000 times higher!