What will be the voltage drop across your power LED?
For example: Whatever voltage you apply, Input voltage = Voltage drop across resistor + voltage drop across POWER LED.
Voltage drop across power LED remains the same(check the datasheet of the POWER LED). you have to consider only one thing, your resistor must have the higher wattage value. So that it can dissipate the power. So choose the resistor value with higher wattage when more voltage you applied at input.
Input voltage is not of concern for an LED. The forward current is what is very important. However, you can use the following formula to find the forward voltage of a LED:
V = (h x c) / (λ x e)
where h = Planck's constant
c = speed of light (m/s)
λ = wavelength of light emitted (meters)
e = charge on an electron (coulombs)
From the data you have given, with power rating 10W, its quite obvious the forward voltage is 8-9 V, as 8V power led's are quite common and may need a heat sink if not provided with it. Now the 8v led's have a forward current rating of around 1A to 1.6 Amperes max.
Really difficult considering the fact that you know only the wattage...however one of my friends told me that certain LED driver that he used for a similar 10W LED had 78 V 120mA output
The trouble with E-Bay parts is that they have no detailed datasheet.
The LED with 8 segments probably has four 3.2V to 3.8V LEDs in series and another 4 parallelled. Then it needs 12.8V to 15.2V. You don't know its actual voltage requirement.
As it heats its current increases if it is not regulated which makes it heat more which increases the current more until it burns out.