ANSWER: 4

EXPLANATION:
This requires some high school algebra. First, let's call the two numbers X and Y, where X is the larger number. We therefore are given that X-Y=1 and X*Y=1. We can then use the first equation to solve for X in terms of Y (X=Y+1) and plug this value of X into the second equation yielding a quadratic equation for Y: Y2+Y-1=0. We can then use the quadratic formula to solve for Y, yielding two values for Y, one of which is negative and thereby eliminated. The remaining value for Y is (-1 + √5 )/2. We now solve for X using the fact that X=Y+1=(1 + √5)/2. We then cube both X and Y and the difference is 4.