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Four pin 5mm LED which has a common cathode part number RL5-RGB-DCC

RED typ 2.0V IF=20mA

GREEN typ 3.5V IF=20mA

BLUE typ 3.5V IF=20mA

Driving from Arduino PWM. I know I need a resistor but do I need one on common cathode, or do I need individual ones for each color?

It depends: if you're trying to drive all three LEDs at the same time, you need individual resistors. Pros: no need to worry about avoiding overlapping on-periods, and maximum possible brightness. Cons: need 3 resistors.

But if you're willing to drive them one at a time, you could possibly get away with just one resistor on the common cathode. Pros: just one resistor. Cons: have to scale PWM max to not over-drive the red LED, and need to synchronize in software so that you're only driving one at a time, and are limited to partial on-period for each LED.

My strong recommendation would be to use three individual resistors for the three LEDs; there's almost no situation in which it'd be a good tradeoff to save a penny on two extra resistors due to the extra complexity and limitations.

Here's why you need different resistors: because if you try to drive both LEDs at the same time with only a single resistor, the one with a lower forward voltage will "steal" current from the other LED, effectively turning it off or making it very dim.

Take a look at this simulation:

D1 has VF=2.04 volts @ 20mA

D2 has VF=1.36 volts @ 20mA

so when both V1 and V2 are on (think of this as your microcontroller pin or PWM output trying to drive both at the same instant), D1 basically doesn't get any current at all. This may not what you expect -- so use individual resistors!

This is sort of a generalization of the "path of least resistance" idea; while not strictly a resistance, the two diodes represent two parallel paths of current flow toward R1. Just as in the case where two parallel resistors will show a resistance dominated by the smaller resistance (because they have the same voltage drop across them, so whichever one allows more current flow at the same voltage drop will dominate the total current flow).

You will need three resistors because the diode voltages differ. A 5V Arduino should be able to drive the LEDs though you will need to choose the resistor values carefully. Measure the resistor voltage drops at full on, calculate the current and adjust the resistor values if necessary. If you have a 3.3V Arduino then you need a higher voltage supply and buffer amplifiers to drive the LEDs.