The number of days since I was born is approximately the number of days in (cube root of year) years (ingnoring leap years), and today is the (cube root of year)$^{2}$th day of the year.

It is also worth to mention that the date format of my DOB (Date Of Birth), written in MM/DD/YYYY is that DD is the $n^{th}$ Fibonacci Number, $n$ is the value of MM, and YYYY is the product of MM, DD, and the cube root of the year.

What date is today and what day I was born?

Hint:

Today's date falls one day earlier than the day of the week I was born.