I currently have 1 RGB led [acting as an output] with its 3 pins (R,G and B) connected to three PWM pins using the appropriate resistor ( resistance calculated according to Vf for each R, G and B). This part is working fine.
Now I want to have 2 other RGB leds (just to increase the brightness of my output). Now I am debating if I put two other RGB led in parallel using the same three resistors or each single pin have its own resistance that is three similar resistances for each Red pin and so on.
Currently
pin, Resistance,LED
O------[]-------|>------GND
O------[]-------|>------GND
O------[]-------|>------GND
A seperate resistor for each is preferable as you cannot guarentee that each LED has the same forward voltage (e.g. the two red diodes might have a different Vf and so on). If they are slightly different, then one of the LEDs will drop the majority of the current which will have one of two outcomes: (i) one is brighter than the other, but all is well, or (ii) the first blows up from passing two much current which in turn leads to the second blowing up from too much current.
"as you cannot guarentee that each LED has the same forward voltage "
Is that possible even if I am using 3 identical RGB leds?
Also I am thinking that this set up will increase the current drawn out of the pin where any single color pin is attached and might blow up the arduino.
You will draw more current from the pin yes, in which case you may be better off using a transistor to drive the leds.
They may be the same LED - bought together, same part number, etc. but they still may not be identical. The forward voltage depends on the atomic structure of the LED, and the amount of 'dopant' in it. Unless this is identical, the LEDs will have a different Vf.
Now most of the time, the variation is so small that it can be ignored, and that may well be the case here, in which case a single resistor would be fine. The best way to check is to connect both up to seperate resistors and measure the voltage across each LED. If they are within a few tens of millivolts, you should be fine with a single resistor. But resistors are so cheap no-a-days, while RGB LEDs are expensive, it doesn't hurt to use seperate resistors.