Six LEDs using one 3 V button cell
UPDATE


  I am using CR 2032 


Two CR2032 cells do not have the capacity to power 6 LEDs very brightly for any reasonable amount of time.  

They will work, just a matter of how brightly for how long. 

You need to carefully select the LEDs you use. You want the most mcd intensity. At 20 mA you can get over 20,000 mcd for red and over 15,000 mcd for yellow.  You can run these LEDs a 1 mA and they will still be bright.

END OF UPDATE

You must not be using any resistors.

Each LED needs its own current limiting resistor.  And they cannot be connected in series. 

You problem with the white, the required forward voltage is about 1 V higher for white than red and yellow. 

The problem is the forward voltage of the white LED is likely greater than 3V. 

First deal with the red and yellow.  I am taking the safe road and assuming the LEDs are 20 mA and the red and yellow forward voltages are 2V. 


Source: Hobby Hour LED Calculator





Now for the white you can try a 10Ω resistor and check the brightness.  You may be able to get away with no resistor so if the 10Ω is too dim you can try no resistor.  

The red and yellow need resistors for sure.

You can measure the voltage across the leads of the red and yellow LEDs to get the actual forward voltages, then use those voltages in the resistor calculator.  Not likely to make that big of a difference. 

If you want the brightness of each LED to be at the same intensity you will need to adjust the current based on the lumen output of each color.