Hi, The relay boards I am familiar with use MUCH less current for the optoisolator signal inputs.
What I measured is on the schematic here: http://goo.gl/cIrjN (Scroll down): 2 ma
So the Mega should not have a problem...
You DO need to provide a separate 5V supply for the relays themselves and their driver transistors.
NOTE: Each relay draws about .08A (80 Ma) when on, so if all 8 relays are actuated the board needs about 8*80 or 640 Ma (.64 amps).
But unless you are are going to activate more than 1/2 the relays at once, this should do it:
http://goo.gl/kfn5K
To keep from going crazy with all the wires, I suggest you use a MEGA Sensor Shield
http://arduino-info.wikispaces.com/SensorShield (Scroll down)
...and cables made up from strippable flat cables like the ones shown here:
http://arduino-info.wikispaces.com/ArduinoPower#4-8
DISCLAIMER: Mentioned stuff from my own shop...