Achieving "white" involves quite a bit of effort.

Strictly speaking, there is no single definition of what is "white". Just look at this article on Wikipedia to learn more about the different kinds of white that are recognised.

Once you know which white you want, you can begin the process of producing it using an RGB LED. 

Each RGB LED contains three individual color LED (red, green and blue), and each one emits light of slightly different intensity for the same amount of current at a specific wavelength.

The process I outline below is a relatively simple way by which you can find out the "perfect" resistance for each color diode.

  1. Replace the fixed resistors with potentiometers.
  2. Manipulate the potentiometers until they produce the shade of white you want.
  3. Remove the potentiometers from the breadboard and measure the value of each pot using a multimeter (the more accurate it is, the better will be for the next step).
  4. Replace the potentiometers with a fixed resistor of exact value you measured. You may need to create networks of those resistors in the (likely) event that you don't have the exact value in a single package. In order to recreate the shade of white that you settled to using the potentiometers, the fixed resistor replacement should be of the same within a very small margin of error (say, less than 1%).

As you can see, it is a tedious process, and in most cases, if we want pure white, you should use a pure white single LED.