Question 611580
A(5, 12, 12) and B(20, 28, 24). 
<pre>
The cube will be smallest if AB is an edge rather than a diagonal.

The distance from A to B is found by the distance formula in 3-dimensions:

d = {{{sqrt((x[2]-x[1])^2+(y[2]-y[1])^2 + (z[2]-z[1])^2)}}} 

d = {{{sqrt((20-5)^2+(28-12)^2 + (24-12)^2)}}}

d = {{{sqrt((15)^2+(16)^2 + (12)^2)}}}

d = {{{sqrt(225+256 + 144)}}}

d = {{{sqrt(625)}}}

d = 25

So each edge of the cube will be 25, and the volume is
given by the formula:

V = E³ where E is the length of an edge, or

V = (25)³ = 15625 cubic units.

Edwin</pre>