For thus we say that He both suffered and rose again, not as though God the Word suffered in His own Nature either stripes or piercings of nails or the other wounds (for the Godhead is Impassible because It is also Incorporeal), but since that which had been made His own body suffered these things, He again is said to suffer for us, for the Impassible was in the suffering Body. (St Cyril's First Letter to Nestorius, here).
According to Cyril of Alexandria, at Calvary, "the impassible was in the suffering Body". In so saying Cyril rightly affirmed the impassibility of the divine Word and also took into account that the Word made flesh suffered for us in his humanity. This is where the communicatio idiomatum or 'communion of attributes' in the incarnate Son comes into play. That which was true of Jesus only in his humanity, i.e. he suffered and died, was not an act of his human nature per se, but the act of the person of the Son in and through his humanity. It is not sufficient to say that the divine nature of the Son remained impassible, while his human nature suffered on the cross. Rather, it was the case that the person of the Son of God suffered for us in his humanity, Galatians 2:20.
When theologians speak of the 'passive' obedience of Christ at the cross, as distinct from the 'active' obedience of his life, it is not meant to suggest that Christ was inactive at Calvary. When used in this context, 'passive' means 'suffering', in the same way that 'impassibility' means 'without suffering'. However, we must remember that the whole of Jesus' incarnate life involved suffering (Hebrews 5:8), and that his death was a positive act of obedience (Philippians 2:8 cf. John 10:17-18). In the words of B. B. Warfield, 'His very passion was his own action.' (The Person and Work of Christ, p. 134, P&R).
This is important, because we should not think of Christ as a mere victim of suffering. The Son did not suffer on the cross primarily in order to show empathy with a world racked by pain and tragedy. Certainly, Jesus our great high priest is able to sympathise with our weaknesses, (Hebrews 4:15). But his cross was not so much an act of divine identity with a suffering world, as divine self-substitution for a guilty world. The good news is this: "Christ died for our sins according to the Scriptures" (1 Corinthians 15:3 cf. 1 Peter 3:18).
What we sinners need above above all else is not the sympathy fellow-sufferer, but the salvation accomplished by a substitute-sufferer. Jesus' cry on the cross was not, "Now I know how you feel!", but, "It is finished!". We are saved by the impassible passion of the Word made flesh and crucified for us at Golgotha.