Thank you very much Efe_114, that was what I thought. I've already tried to remove the base resistor and the leds became slightly more bright but not enough. Will the darlington pair have some disadvantages (current consumption and/or voltage drops)? Can I connect them straight together without any additional resistor?
I've also tried the schematic that bigclive did in this video and it did't work either. Also it seems that the diode is connected in the wrong direction, but in his video everything worked perfectly.