The short answer is: you should use a resistor for each LED.
You can use a reasonable value resistor (like 500 ohms or 1k) in series with the power supply to find out the voltage of the LED (measure it directly across the two leads) but there is no real way to see how many milliamps it can take.
Different colour LEDs will often have different forward voltages, so running them in parallel (without their own individual resistor) will result in the LEDs with lower forward voltage dissipating more power. IOW, your red LEDs would be overly bright, possibly even to the point of failing, while your blue LEDs would be dim, maybe not even lighting at all.
One resistor for each LED.
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