Exactly.
So it's all in the code. So we need to talk about your code. Where is it?
BTW, read the forum instructions in order to know how to post code here.
That is a very confused statement! 
An Arduino Mega 2560 does not, cannot ever power anything! It is a microcontroller board, never a power supply. digitalWrite is what your code uses to send data (though the FastLED library presumably bypasses that extremely slow function) via microcontroller pins, nothing whatsoever to do with power.
Even if it were appropriate - it clearly is not - to switch the power to your LED strip, you would need a FET suitably rated for the substantial operating current of the strip. But that would get you nowhere as you still need to re-program the strip whenever you turn it on.
Do note however, that with all black programmed to the strip, it does still draw about 1 mA per pixel; 300 mA for a 300 pixel strip.