Problem of the Week 27

The difference of two cubes is 56,765.  What two positive integers satisfy this condition?


Alternate Problem 27

The volume of the larger rectangular box shown below is three times the volume of the smaller rectangular box.  What is the value of x?


Extension Problem 27

The expression x2  + y2 is not factorable over the real numbers.  Can x3 + y3 be factored?  If so, what is the factorization?