By what factor does the moment of inertia i2 of sphere 2 exceed the moment of inertia i1 of sphere 1?

In fact the mass of Sphere 2 will be 2³ = 8 times the mass of Sphere 1 (both spheres are steel and therefore will have the same density). 
Therefore, since they were both steel then the larger one would have a mass of 2^3 or eight times the smaller (v is proportional to r^3). So the larger one would have an I 8*4 or 32 times the smaller one.
We let M equal to the mass of the first sphere then the mass of sphere 2 will be 8M and your calculation will result in this: 
I2 = 2/5 (8M)(2R)² = 2/5 8M 4R² = 32(2/5 M R²) 
so ration I2/I1 = 32.

The answer you are looking for is 
2.953125
2 

hope that