Today’s date is 56/18/2197 and the day you were born was 8/21/2184.
I utilized excel formulas to quickly guess and check different cube years for today. See below for the formulas and solve process. The main part to check was the factors of born yyyy/C, as those needed to be Fibonacci n and nth number, and multiply back to born yyyy. You can narrow the search by knowing the Fibonacci numbers are constrained to properly formatted dates.