Please help, I can't seem to figure out the answer to this homework question

Question

This is the question:

 In a last-ditch attempt to increase their budget, science teachers at CDDHS cast small solid bronze busts of their principal for sale to students as doorstops, paperweights, etc. One order, in suspiciously familiar handwriting, came in for a bust that would be identical except for scale: it was to stand four times as tall as the standard model. How many of the small busts did the teachers have to melt down to cast this big one?

Answer 1

I hope you would be able to answer the question if it were not busts,

but cubes. The question would be:

"How many small cubes would you need to melt to get a cube four times taller."

This is how you think of this question:

Suppose the small cubes have volume a×a×a = a³

The the big cube then has volume (4a)×(4a)×(4a) = 64a³

In other words, it would take 64 small cubes to make the big one.

And that how it works for all three dimensional objects that are resized

keeping their shape.

When a linear dimension increases by a factor of k, their volume increases

by the factor k³.

If you understand why it works for cubes, but not for irregular objects,

imagine the irregular object composed of many tiny cubes.

When you increase the linear dimension of the irregular object by a factor k,

each of the tiny cubes gets increased by the same factor.