I think the OP wants a simpler way than analog write. Aqua is Blue+Green, Yellow = Red+Green, and Purple=Red+Blue.
Something like this might suffice (not compiled or tested):
const int BluePin = 9;
const int GreenPin = 10;
const int RedPin = 11;
const int IncrementButton = 2;
int colormode;
void setup(){
pinMode (BluePin, OUTPUT);
pinMode (GreenPin, OUTPUT);
pinMode (RedPin, OUTPUT);
pinMode (Incrementbutton, INPUT);
}
void loop(){
switch (colormode){
case 1: //white
digitalWrite(BluePin, HIGH);
digitalWrite(GreenPin, HIGH);
digitalWrite(RedPin, HIGH);
break;
case 2: //red
digitalWrite(BluePin, LOW);
digitalWrite(GreenPin, LOW);
digitalWrite(RedPin, HIGH);
break;
...
...
case 5: //aqua
digitalWrite(BluePin, HIGH);
digitalWrite(GreenPin, LOW);
digitalWrite(RedPin, HIGH);
break;
case 6: //yellow
digitalWrite(BluePin, HIGH);
digitalWrite(GreenPin, HIGH);
digitalWrite(RedPin, LOW);
break;
...
...
ect...
}