... I'm currently working on a project and the electrician has rob the wrong cable to some hotel rooms. It should be a 6 core to light up the three difrent LED's, they have basically run a two core.
Is there a way to make this work using resistors or a circuit? ,,,
You can do a LOT of things with resistors and a circuit, but I am confused by your terminology. Does "6 core" mean six individual wires while "two core" means a single pair of wires? If so, the answer depends on how you want to "light up the three difrent LED's". Do these LEDs light up one at a time, with only one LED illuminated at a time? Or are there situations where one, two, or all three LEDs light up at the same time? Since you said "it should be a 6 core" circuit, I assume you intended to dedicate two wires for each LED and have the LEDs operate independently so that one, two, or three LEDs can be illuminated simultaneously and independently.
If that is so, you may have to resort to a complicated solution that involves coding and decoding the electrical "signal" applied to just two wires. Instead of doing that, I would first ask the electrician to come back and install two more wires for a total of four wires: one wire for common, one wire for each of the three LEDs.
If adding two more wires is impossible because of budget constraints or accessibility to install the additional wiring, you could encode eight different voltage levels on two wires using three binary-weighted switches. A simple op-amp circuit that sums the three switch closures from a constant-voltage source through binary-weighted resistors would then (for example) produce output voltages of zero, 1, 2, 3, 4, 5, 6, or 7 volts, representing switch closures combinations of 000, 001, 010, 011, 100, 101, 110, and 111. At the other end you would need to "decode" these eight voltages into three LED illumination commands. All this is way more complicated than adding two more wires, but you do what ya gotta do to make things work... even if the result is a kludge. Been there, done that, try not to do it again.