Show that there are positive integers A, B, C and D such that A! B! = C! D! and A + B = N^3.

(Here A!, called the factorial of A, is the product of all the positive integers up to and including A, so that 4!=1×2×3×4=24.)

For example, if N=2 then N^3=8, and we find 3! 5! = 1! 6! and 3 + 5 = 8.