why we say that in three phase system total power delivered to the balanced three-phase circuit is the same at any instant
It comes down to the fact that in an ideal system, each phase has a sine waveform, and the well known relationship 

$$sin(x)^2 + cos(x)^2 = 1 $$
for all X, and power is proportional to V^2.

Now that relationship obviously applies to 2 phases 90 degrees apart. How can you apply it to 3 phases 120 degrees apart? 

Take the first phase as Sin(X). The other two are $$sin(x + 120 degrees)$$ and $$sin(x - 120 degrees)$$

A bit of vector analysis (draw the three out to illustrate) lets you resolve each of the latter two phases into sine and cosine components.
So $$sin(x + 120) = A * sin(x) + B * cos(x)$$ I'll let you figure out the values of A and B.

Repeat for the other phase $$sin(x + 120) = C * sin(x) + D * cos(x)$$

Now square each of the three phases and sum over the squares... this is a bit of an exercise, but you should get

$$sin(x)^2 + cos(x)^2$$

which is of course 1.