1 Watt over the LED would mean:

Based on your readings,
2 Watt = 6v * I
I = 333mA
6v/333mA = 18 Ohms (That's resistance of the LED)

1 Watt = I^2 * 18 Ohms
I = 235mA

6v/235mA = 26 Ohm resitance
26 - 18 = 8 Ohm resistance in "mystery" circuit.
6v - 8v*235mA = 4.12 V over the LED