Externally powering a series of LEDs at maximum brightness with 470 ohm resistors and fading capabilities
From the datasheet
LED Imax = 20 mA.
LED Vf (forward voltage) = 2.0 to 2.5 Volt
Assume the Arduino and LEDs operate on 5V.
This assumption can be altered.
For a series LED resistor  Vr = 5V - Vf = 2.5 to 3V.
The resistor will drop this voltage when LED current flows through it.
R = V/I = (2.5 to 3V)/I
Assume 20 mA and 3V to start.
R = V/I = 3/0.020 = 150 Ohms.
Here is a basic circuit.
You can use 1 LED or many per circuit - each with its own resistor.
You can have a number of these circuits - each with its own PWM pin.
Q1 can be almost any cheap bipolar transistor.
I've shown a BC337-40 which is superb and usually low cost = but many others work OK.
R1 at 10k will work for multo LEDs per transistor at 20 mA.
With large numbers it could be smaller - eg 3k3.
When PWM input is high Q1 is turned on and the LEDs light.
PWM low -  LEDs off.



simulate this circuit &ndash; Schematic created using CircuitLab