There is a total 200ma current limit for all output pins (plus chip overhead) combined continuous current, so this is a "problem load" unless you use external switching transistors for the leds.
That is not correct. The '2560 can accomodate 800mA; 200mA/Vcc pin.
See Notes 3 & 4 under the table in Section 30 of the datasheet for how the current must be spread out:
3. Although each I/O port can sink more than the test conditions (20mA at VCC = 5V, 10mA at VCC = 3V) under steady state
conditions (non-transient), the following must be observed:
ATmega640/1280/2560:
1.)The sum of all IOL, for ports J0-J7, A0-A7, G2 should not exceed 200 mA.
2.)The sum of all IOL, for ports C0-C7, G0-G1, D0-D7, L0-L7 should not exceed 200 mA.
3.)The sum of all IOL, for ports G3-G4, B0-B7, H0-B7 should not exceed 200 mA.
4.)The sum of all IOL, for ports E0-E7, G5 should not exceed 100 mA.
5.)The sum of all IOL, for ports F0-F7, K0-K7 should not exceed 100 mA.
If IOL exceeds the test condition, VOL may exceed the related specification. Pins are not guaranteed to sink current greater
than the listed test condition.
4. Although each I/O port can source more than the test conditions (20mA at VCC = 5V, 10mA at VCC = 3V) under steady
state conditions (non-transient), the following must be observed:
ATmega640/1280/2560:
1)The sum of all IOH, for ports J0-J7, G2, A0-A7 should not exceed 200 mA.
2)The sum of all IOH, for ports C0-C7, G0-G1, D0-D7, L0-L7 should not exceed 200 mA.
3)The sum of all IOH, for ports G3-G4, B0-B7, H0-H7 should not exceed 200 mA.
4)The sum of all IOH, for ports E0-E7, G5 should not exceed 100 mA.
5)The sum of all IOH, for ports F0-F7, K0-K7 should not exceed 100 mA.
If IOH exceeds the test condition, VOH may exceed the related specification. Pins are not guaranteed to source current
greater than the listed test condition.