By the assumption that you are reading this topic because you need the highest brightness from white LED, so to create a DIY headlight, the tip below it is the solution.
Only if you play with some LED and conduct your own experiments you do realizing the limitations of LED.
I did made a DIY power pack with lithium batteries and protection controller that outputs 16.8V and eventually drop down and CUT off at 11V.
I made it so to add this on my bicycle so to become an rechargeable source that will handle head lights and tail lights.
After doing so, my first need was to modify the ordinary 3.3v 0.3A headlight by installing LED capable for 12-16V.
Many months back I did purchase 50 X 5mm White LED 18000mcd
Their specifications are 3.2V 20mA
My first experiment was to solder five LED in series, the experiment shown that LED can handle the voltage that way but the problem is that the current flow it is limited (by all this LED in series) and their brightness is not as it should.
By using multiple multimeter for voltage and current measurements I did realize that the proper way to do that is by connecting them in parallel, and to limit the voltage by resistors.
By connecting them as shown in the schematic bellow, I did manage to achieve the specification of 3.2V 20mA for its LED, in my headlight I use six LED and the total consumption is now 120mA = success.
The resistors that I use are 1/4W 2x 330 Ohm in series.
They get warm but not that hot as by using a single resistor of 330 Ohm.
The point is that I got lucky by using the right resistor value in my second attempt, and now I very happy that my conversion succeeded.