Well, no. But that's only because the superstitious in the US only recognizes the US date format so that todays date is 61408 or even 80614, both of which are obviously a lot less exciting. For one, there's fewer numbers in them than 140608 and their cubic roots are no magic integer numbers like 52. Also note that 52 is the number of weeks in a year, so it's obvious that 140608 is an *incredibly* special day - watch out!
The next cubic day, if we survive this one, will be 9 November 2025 (91125 = 45^3) and the last one was 11 May 1995 (110595 = 48^3).