What are the exact current carrying capacities of 4 sq. mm. & 6 sq. mm. copper cables

What de-rating factors apply to the copper conductor cables?

Since we don't know what you are really trying to accomplish:
1. I would first convert sq. mm to AWG since I don't work in sq. mm.

http://www.reuk.co.uk/AWG-to-Square-mm-Wire-Size-Converter.htm

2. Use a wire ampacity calculator to get your answers.
http://circuitcalculator.com/wordpress/2007/09/20/wire-parameter-calculator/

Hope this helps.

Rick's answer is 100% correct.

Were you to install a PVC/PVC cable of a particular CSA in free air, it might have a current rating of 10 Amperes if the ambient air temperature does not exceed 70 degree C. If as little as 500mm of the length of that cable was covered in thermal insulating material, its current would fall to 5 Amperes. An un-insulated copper cable of the same CSA, supported in free-air on poles or pylons, might have a current rating of 40 Amperes in a particular ambient temperature.

The rating and de-rating of conductors is aimed at preventing heat damage to the cable's insulation and at preventing fires.

There is not an exact answer. Power loss in a wire is I^2 R. This causes the wire to heat up. Now the issue is how hot can the wire get and still be safe. Well, this depends on the insulation and the cooling of the wire. Is it in a bundle? Is it in free space? Or what?

Wire current rating tables are based on certain assumptions regarding the above questions. The assumptions should be given, but they may not be. Find out what they are.