Do 3 Phases in a 4 Core Cable Cancel Each Other’s Magnetic Flux? Heating Issue Explained

Do 3 phases in a 4 core cable cancel each other's magnetic flux? 
Secondly I have observed that a 4 core cable whose 3 wires are connected to a single phase and 4th is connected to neutral in a transformer, heats severely ( even burning out at normal loads). Is it because the flux don't cancel, as is in the case when different phases pass.

Umer...yes the magnetic flux should cancel in a 3-phase cable as the currents in should equal the currents out, even with unbalanced loads.  Because of wire spacing you will always get a bit of residual flux but I don't think that is your problem.With a balanced 3-phase load the current in your neutral conductor should be Zero. But with a severely unbalanced load (only one or two phases passing all the current) the currents in the neutral conductor can be very large.  So look for unbalanced loads, also you may have a cable with a smaller neutral conductor than the main phase conductors, which will exacerbate the problem.

As David Ashton states, for balanced 3-phase resistive loads, the currents are sinusoidal, and the currents tend to cancel in the neutral conductor.For loads that draw mostly third-harmonic currents, the currents tend to add in the neutral conductor.In your 4 core cable, what is the current rating of your neutral conductor, and what is the single-phase load current you are running?

Yes neutral is small while other 3 wires are larger in diameter plus they all are carrying same current because of connection to the same phase so while combined they are much larger than one smaller neutral wire.

It's 3×300mm and 1×150mm  copper cable and current on each of three wires is around 220A carrying same phase current. 4th conductor which is half of diameter was used as neutral but when this neutral wire was disconnected cable became normal in temperature. 

Thanks David for your response. Let me explain you the situation. Six wires (3×300mm/ 1×150mm sized) are being used means that 2 wires for each phase i.e, six 300mm conductors. All of these six 4 core cables have a smaller (150mm) conductor which is connected to the neutral of transformer. So neutral current is devided between 6 conductors one from each wire. The heating problem was solved as soon as the neutrals from these wires were removed and a new separate wire was used for neutral.Secondly what do you mean by current in and current out are equal? Because in three phase all the phases have currents in same direction i.e, towards the load!