Correct on the derating issue,dmatos. I almost mentioned it, but thought why give the OP any ideas. But since you brought it up,bundling cables needs special consideration.
Derating is done by adding up the total amount of current carrying conductors. With the typical two and three wire cables , plus the ground each wire not a ground is a current carrying conductor. To start, for example, when 4-6 current carrying wires are bundled, and this happens just with two 2 wire cables, must derated the circuits by 80%. The derating percent lowers as the amount of wires increase.
The method of derating is done by one of two ways. Either increase the size wire, or reduce the size/rating of the overcurrent protection device(fuse or circuit breaker).
Derating can get a bit complicated, as the ampacity to start the calculations of the wire begins with the type of insulation.
Better to not bundle any cables and not have to deal with derating at all.