According to Orthodoxy :
God suffered and God died on the cross... from the series of hypostatic union..
the hypostatic union says that the two natures of Christ were united in his Divine hypostasis... meaning that his human nature was(is) part of his Divinity.. so humanity being a part of the divinity, which the divinity assumed, we can say that yes God suffered and yes God died on the cross... The suffering and death of Christ were real... he assumed humanity in all ways.. yet if we want to be more edgy...
from the series of Holy God , Holy Immortal , the Divine essence of Christ did not suffer or die in any way, but his human essence did... he suffered and died in his humanity , His divinity remaining incorrupt and imuable, as part of the One True God...