Electrical – How to calculate the resistor value for a bicolor led

The 20mA rating of your LEDs is probably the recommended maximum current. Most LEDs will produce light at much lower currents - I find 5 mA is sufficient for indicator light use.

Try the LEDs with different resistors to see what current is actually required to produce sufficient light for your application (more current = brighter light).

Also, check the maximum current the Pi GPIO pins can handle - I have a feeling it is less than 20 mA, but can't check at the moment.

To start, Some of your math is a little off.
For the red LED, if you are using a 5v supply and the red LED needs 20ma and has a voltage drop of 2.1v, then you need a limiting resistorstrong text of (5-2.1)/.02 = 145 ohms.
For the green LED, you need (5-3.2)/.02 = 90 ohms.
For the blue LED, you need (5-3.1)/.02 = 95 ohms.

Assuming that these resistors cause equal LED illumination, and that the light intensity varies directly as the current applied to the LED, then you need to reduce the currents to the green and blue LEDs as follows:

For the green LED, the current needed is (20ma x 20% =) 4ma. For the same voltage drop, the new current limiting resistor required is (5-3.2)/.004 = 450 ohms.
For the blue LED, the current needed is (20ma x 15%) =) 3ma. For the same voltage drop, the new current limiting resistor required is (5-3.1)/.003 = 633 ohms.

Obviously, if the assumptions are not accurate, the calculations will also not be accurate. If more accuracy is required, then you will need to use the LED's data sheet.