The answer to this question is based on an understanding of sin and God's holiness.

Sin is defined by its relationship to God's law and His moral character. It is the failure to conform to the moral law of God in behavior, attitude or nature.

The Bible speaks of sinful behavior:

The Bible speaks of sinful attitudes:

"You shall not covet your neighbor's house; you shall not covet your neighbor's wife or his male servant or his female servant or his ox or his donkey or anything that belongs to your neighbor." (Ex 20:17)

You have heard that it was said, "You shall not commit adultery"; but I say to you that everyone who looks at a woman with lust for her has already committed adultery with her in his heart. (Matt 5:27-28)

The Bible speaks of how sin was introduced into the world and became a part of human nature:

Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned. (Rom 5:12)

Among them we too all formerly lived in the lusts of our flesh, indulging the desires of the flesh and of the mind, and were by nature children of wrath, even as the rest. (Eph 2:3)

The holiness of God is defined as the separation of sin from God.

Anything that God comes in contact with on earth is consecrated, set apart and made holy for the service of God. While there is a prescribed responsibility for human beings, it is God who makes something holy.

The angel of the Lord appeared to him in a blazing fire from the midst of a bush; and he looked, and behold, the bush was burning with fire, yet the bush was not consumed. So Moses said, "I must turn aside now and see this marvelous sight, why the bush is not burned up." When the Lord saw that he turned aside to look, God called to him from the midst of the bush and said, "Moses, Moses!" And he said, "Here I am." Then He said, "Do not come near here; remove your sandals from your feet, for the place on which you are standing is holy ground." (Ex 3:2-5)

It shall be a continual burnt offering throughout your generations at the doorway of the tent of meeting before the Lord, where I will meet with you, to speak to you there. I will meet there with the sons of Israel, and it shall be consecrated by My glory. I will consecrate the tent of meeting and the altar; I will also consecrate Aaron and his sons to minister as priests to Me. I will dwell among the sons of Israel and will be their God. (Ex 29:42-45)

Through this understanding of sin and the holiness of God, Jesus' work of atonement can be examined. The aspect of atonement of interest is substitution, which can be seen from two perspectives.

From a human being's perspective, Jesus took our place of judgment for each one of us as individuals. Jesus' death on the cross brought us into God's favor and reconciled our relationship with Him. Because of Jesus' obedience to God's will, Jesus' righteousness is imputed on us.

And when He had taken some bread and given thanks, He broke it, and gave it to them, saying "This is My body which is given for you; do this in remembrance of Me." And in the same way He took the cup after they had eaten, saying, "This cup which is poured out for you is the new covenant in My blood." (Luke 22:19-20)

For the love of Christ controls us, having concluded this, that one died for all, therefore all died; and He died for all, that they who live should no longer live for themselves, but for Him who died and rose again on their behalf. (2 Cor 5:14-15)

More pertinent to the question of cost is looking at Jesus' substitution from God's perspective. Here Jesus' substitution, following Levitical sacrificial laws, was indeed sacrificial and paid God's judicial price in full and satisfied God's just wrath. By standing in the place of human beings, Jesus assumed our past, present and future sins and bore its penalty.

He made Him who knew no sin to be sin on our behalf, that we might become the righteousness of God in Him. (2 Cor 5:21)

and walk in love, just as Christ also loved you, and gave Himself up for us, an offering and a sacrifice to God as a fragrant aroma. (Eph 5:2)

While one may gain a sense of cost by observing the sacrifice of Jesus' life by crucifixion, less obvious to perceive is the cost to God Himself. Jesus' substitution brings sin within the proximity of God's triune Being which cannot be tolerated. In judgment of sin, at the time of crucifixion, God requires the death of Jesus. Presumably, while it is the human aspect of Jesus that is sacrificed, some sort of separation occurs within the triune being of God:

About the ninth hour Jesus cried out with a loud voice, saying, "ELI, ELI, LAMA SABACHTHANI?" that is, "My GOD, MY GOD, WHY HAVE YOU FORSAKEN ME?" (Matt 27:46)

At the ninth hour Jesus cried out with a loud voice, "ELOI, ELOI, LAMA SABACHTHANI?" which is translated, "My GOD, MY GOD, WHY HAVE YOU FORSAKEN ME?" (Mark 15:34)

It is difficult to understand Jesus' cry of being forsaken by His Father. Yet, in this context, one can get a sense about the cost to both God the Father and Jesus the Son.

There is a real cost to atonement beyond the physical suffering of Jesus on the cross. God the Father willingly provides His only Son to be in part a human being, allows His Son to experience the agony of crucifixion, and physically separates Himself from the sins that Jesus bears.