I am not sure but I think Arduino Mega 2560 board is designed to handle a voltage range of 7-12V, as stated in the official documentation. The DC jack is connected to a voltage regulator on the Arduino board, which steps down the input voltage to a stable 5V
Please keep in mind that any power you provide from the Mega will be coming through that regulator, and the more power you take from the board, the hotter that regulator will get.
So… don't take too much power at all from the board for you external circuits, and put your finger on the regulator once in a coffee break or so and see that it is, if at all warm it's just warm and not HOT.
Sometimes: people leave that power method unused, and deliver 5 volts directly from a real power supply of 5 volts.
Also, you can lower the Mega board through the USB connector. A USB cable and a phone charger make a nice power supply.
The more current you draw (in your case, the more LEDs) the more power the voltage regulator has to convert to heat. And with barely any heatsink, it will eventually overheat.
You will have to do some calculations. if you take a worse case scenario where each LED draws 20 mA and they are all on, that 120 mA will go through the voltage regulator. With a 7V power supply, the voltage regulator will have to dissipate (7V - 5V) * 120 mA equals 240 mW. With a 12 V power supply, the voltage regulator will have to dissipate (12V - 5V) * 120 mA equals 840 mW. And the latter is more than likely too much.
You also need to beware be aware of the maximum current that can go through the main processor
20 mA safe maximum for a pin.
100 mA maximum for a port.
200 mA maximum for the processor's Vcc and GND.
So choose your current limiting resistors carefully
I so confirm.
If that's what you're doing then that's fine.
Why not run power via the USB jack?
If you have one of these (or something similar), use it --