Apparently, somewhere in the vicinity of 0.04W, so i wouldn't even waste time thinking about it... You've probably wasted way more pwer typing and reading in this thread than your leds will use over the next couple of months
https://answers.yahoo.com/question/index?qid=20080706220639AAowWePThe color and type determines the reqruired voltage. This ranges from 1.8V for a certain red, through 2.4V for reds, oranges, greens, yellows. Violet, UV, blue and white go up to about 5V.
Low current LED's go down to 1mA at 1.8V (red) for their rated output, which is 1.8V * 0.001A = 2mW or 0.004W.
Most common LED's use 20mA at 2V or so, so about 40mW (0.04W).
Large LED's can use up to 5V and 0.6A, or 3W, and bigger ones are coming out all the time. The voltage pretty much stays the same, but the current goes up.
The circuits used to drive LED's do not always supply full voltage and current. If less voltage and current is supplied, the power is less. Resistors are often used to limit current to the LED so it is not destroyed.
Everything else being equal, 10 diodes will indeed use 10x as much power.