My partner and I tried to have “When I’m Sixty-Four” played at our wedding, but we didn’t because I couldn’t find the sheet music.
It’s my birthday. When I’m sixty-four our second child, who will arrive in a few days, will also have an age which is a cube.
We’ll never be prime at the same time, though.
God plays dice 
Since you’ll have a different birthday from your child, the difference between your ages will change by 1 depending on the time of year. This guarantees that you will eventually both have prime ages (unless you somehow know that one of you will die before that happens).
If we assume you mean that you mean that your ages will never both be prime on your birthday, then I think this must be your 36th or 62nd birthday, so that your child will be 27 or 1 on your 64th birthday and so that the difference between your ages (on your birthday) will be an odd number. I don’t see how to distinguish those two possibilities though.