Careers

We call a date "square" if all of its components (day, month, and year) are perfect squares. I was born in the last millennium and my next birthday will be the last square date in my life. If we sum the square roots of its components (day, month, year), we get my current age. My mother would have been born on a square date if the month were a square number. However, it is not a square date, but both the month and day are perfect cubes. When was I born and when was my mother born?