You are given a cube of length of side 128 units. 

units.

Side (or length) of the cube = 128 units. 

Total Surface area of the cube = 4 * side² = 4 * 128 * 128 = 65536 square units.

Volume of the cube = side³ = 128 * 128 * 128 = 2097152 cubic units. 

Length of the diagonal of the cube = (3 * side²)^0.5 = 221.7 units  (Extending the Pythagorean theorem to three dimensions)

You might also make these calculations by considering the cube to be a special case of other 3D hexahedrons: an equilateral cuboid or a regular square prism or a square parallelopiped. 

A sphere touching all six vertices of a cube is known as its circumsphere. 

The circumsphere of this cube as a radius equal to (length of the diagonal)/2 = 110.85

Now, if we know that the cube is made of Iron and we measure the side in centimetres and the density of the material is 2.7 grams per cubic centimetre, we can calculate the mass of the cube:

Mass of the cube = Density x Volume = 5662310.4 grams. 

Let's compare this current cube (let's call it cube A) with a cube B of side 64 units. 

The scale factor A : B = 128:64

Ratio of surface areas of A : B  = 65536: 16384 = 4 : 1 (this holds true whether you compare total surface area or surface area per side, or any corresponding pairs of surface areas between the cubes)

Ratio of volumes of A:B = 2097152 : 262144 = 8 : 1

What if the current cube is made hollow with a thickness of 2 units?

In that case, the volume of the cubic gap inside the current cube has a size of 126 units. So the volume of the cubic gaps is 126 * 126 * 126 cubic units = 2000376 cubic units.
So the volume of the material used to construct the cube = Volume of the outer cube - volume of the gap = 2097152 - 2000376 = 96776 cubic units.

You may find some more useful notes and information about the cube over here.