Isaiah 9:6 "For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace." 

Regarding the possible confusion on this verse in harmonizing it with the scriptural teaching that Jesus is the Son of God, we observe that this verse is definitely a prophecy referring to Jesus. Jesus is a mighty god, but he is not the Almighty God. Remember that Jesus quoted verse (Psalm 82:6) in reproving the Jews for wanting to stone him for calling himself the Son of God. 

Let us read this account in John 10:31-36: "Then the Jews took up stones again to stone him. Jesus answered them, many good works have I shewed you from my Father; for which of those works do ye stone me? The Jews answered him, saying, for a good work we stone thee not; but for blasphemy; and because that thou being a man, makest thyself God. Jesus answered them, is it not written in your law, I said, ye are gods? If he called them gods, unto whom the word of God came, and the scripture cannot be broken; say ye of him, whom the Father hath sanctified, and sent into the world, thou blasphemes; because I said, I am the Son of God? 

God in this sense means a mighty one. To refer to the one and only Almighty God, we need to add definitive language, like "Almighty." 

So then in Isaiah 9:6 we can see that the phrase "mighty God" does not have to refer to the Heavenly Father, but can and does refer to Jesus. 

Now the phrase "everlasting Father", means agelasting Father in the Hebrew. But the thought of Jesus being a father is of more interest. 

In I Corinthians 15:45 we read "And so it is written, The first man Adam was made a living soul; the last Adam a life giving spirit". As Adam was the father or progenitor of the human family, so Jesus because of his willing sacrifice on the cross, became the second Adam, a life giving spirit for the dying human family. Adam gave us life, but actually we all die because of inherited sin. Jesus though, gives us the ability to gain perfect life and that eternally. 

Similarly we read in Revelation 22:16 "I Jesus have sent mine angel to testify unto you these things in the churches. I am the root and the offspring of David, and the birth and morning star." 

Jesus is the offspring of David in a sense through his genealogy through Joseph and Mary. This fulfills certain prophecies. He is the root of David in the sense that the root is the life source for a plant. Jesus will resurrect David, he will be the life source for David in the future. So then, in effect, Jesus will be a father or life giver to David, but not to David alone, but rather to all mankind, just as the first Adam was to the whole human family. 

We trust that this helps to explain Isaiah 9:6 with the rest of the scriptures in explaining that Jesus is the Son of God Almighty, and that in the peaceable kingdom, Jesus will be the mighty God empowered to restore the fallen human family as his own as the second Adam or second father to the race.