these white LEDs which should be at least 3v or 4v.
Yes, white led's typically have an inherent forward drop of between 3.2V and 3.8V, and 4V is well within the spec at operating current - so this really shouldn't work at all.
In practice, however, I've found
some white LED's will operate down to 2.8V, so it's just possible to run them off a pair of fresh AA batteries. Not for very long, though.
The LEDs can't be getting much power, can they?
That style is rated for about 60mW each, so 64 of them would draw nearly 4 watts, total, at about 1.28A.
Since the voltage is very close to the battery voltage and the loading is high, this is one of a few applications where you can run the LED's without a resistor.
Battery life would be lousy, though. The led's aren't going to run at 2.5V, and there is still considerable power left in the AA batteries when they have a loaded voltage of 1.25V each.