Question

If you cut a metal cube into four pieces, do the new pieces have a different mass than the original cube? Do the new pieces have a different density than the original cube?

Answer 1

Each piece will have 1/4 of the mass of the original big cube, but its density will be the same.
Density is a property of a substance, no matter how much or how little of it you have.
A speck of it on the tip of your pinky and a supertankerful of the same substance have the same density.