This is an excerpt taken from an article in the study of the Book of Hebrews, titled, Hebrews 4:13, The Eyes of the Lord. The full message of the article, of course, cannot be realized by taking a few paragraphs out of context. However, it was necessary to give readers a brief understand of how the numbers of eight and seven are related in this particular context.
God looked down and saw the total depravity of the populace of the earth. Would this be the end of all flesh?
And it repented the LORD that he had made man on the earth, and it grieved him at his heart. (Genesis 6:6)
And the LORD said, I will destroy man whom I have created from the face of the earth; both man, and beast, and the creeping thing, and the fowls of the air; for it repenteth me that I have made them. (Genesis 6:7)
  The race of mankind, as a whole, had come to the end of wickedness. For God was quite ready to destroy all the peoples of the world. They, to a man and woman, had denied God, and were consumed with their own abominations in every form, and manner. Mankind delighted in all their wicked imagination. The whole world had filled up the cup of sin, and drank from this cup until there was no reason, nor wisdom, but only the madness of their sin was evident. One could see that the end was nigh.
But – Grace
  Then the Holy Spirit speaks out in verse 8 of Genesis 6, and we read these words: But Noah found grace in the eyes of the LORD. Notice that this verse begins with the word, but. God presents to us, in all this ruin, one man of faith. The word ‘but’ is usually used to explain or emphasis one’s failure, or a contrast, or an exception. And in this failure of man, God inserts the word ‘but,’ to reveal one man named Noah, and this one man found grace in the eyes of the LORD. This is the first time the word ‘grace’ is mentioned in Scripture. This comes when the whole world is in ruin. Out of the millions of inhabitants there was only one man, and because of this one man who lived by faith, he found grace in the sight of the Lord. It is amazing that the Holy Spirit waits through thousands of years, then in Noah, He pulls this divine word out of His treasure chest, and grace is introduced to man before the flood. But, how can grace overcome such odds? Earth is totally consumed by sin, the creation is reeling and groaning under the heavy weight of the sin of man. God is repentant that He ever made man. He is about to destroy all flesh, and then the glimmer of life. In this darkness, God said, Let there be light, and Noah was the recipient of God’s light. Noah finds grace in the eyes of the Lord. This is more than God just looking on Noah, if we study the eyes of the Lord, we see that His eyes are the very part of His perception of man. His eyes are not like our eyes, for His eyes distinguish between righteousness and unrighteousness, between the holy and the unholy, and between clean and unclean (Ezekiel 44:23). The eyes of the Lord can be a consuming fire, (Revelation 1) and the eyes of the Lord can be the minister of grace. We see both in Genesis, Chapter 6. We have this one man, Noah, living by faith, the recipient of grace in a world that has gone mad with sin. In 2 Chronicles 16:9 (although this verse is recorded much later in the history of mankind) it is truly a reflection of the man called Noah. For the eyes of the LORD run to and fro throughout the whole earth, to shew himself strong in the behalf of them whose heart is perfect toward him. Herein thou hast done foolishly: therefore from henceforth thou shalt have wars. The eyes of the Lord searches this world for those of faith, those whose hearts have believed, and do believe in the Almighty God, and for those who walk by faith, and live in the grace of God. Noah was the only one mentioned who had found this wonderful grace of God. At this monumental time in the history of mankind, Noah was the only recipient of God’s grace. What about his sons, and his wife, and the wives of his sons? There is no mention of grace, nor faith. Why did God bring them through the flood? They were brought through the flood because of the faith of Noah, and because of the grace that God had given Noah. God honored His servant by prolonging the days of those in his family, and bringing them through the flood. They were preserved by Noah’s faith.
By faith Noah, being warned of God of things not seen as yet, moved with fear, prepared an ark to the saving of his house; by the which he condemned the world, and became heir of the righteousness which is by faith. (Hebrews 11:7)
Though these three men, Noah, Daniel, and Job, were in it, they should deliver but their own souls by their righteousness, saith the Lord GOD. (Ezekiel 14:14)
Though Noah, Daniel, and Job, were in it, as I live, saith the Lord GOD, they shall deliver neither son nor daughter; they shall but deliver their own souls by their righteousness. (Ezekiel 14:20)
Why The Eighth?
  The conclusion (by the Holy Spirit) is that Noah walked by faith and found grace in the eyes of the Lord, and seven others were brought through the flood, saved from death because of Noah who Peter called the eighth person in 2nd Peter 2:5. And spared not the old world, but saved Noah the eighth person, a preacher of righteousness, bringing in the flood upon the world of the ungodly;. Once again, as was in the life of Abel, so too, in the life of Noah we see much as the Holy Spirit continually reveals this marvelous life of faith in God. In 2nd Peter if this verse was under the jurisdiction of man, and not the Holy Spirit, man would have called Noah the first person, not the eighth person. But God’s ways are not our ways.
  The Holy Spirit calls Noah the eighth person, the number eight (8) signifies a new beginning. It also signifies the beginning of a new day; and therefore, 
in Noah we see the beginning of a new society after the flood. We must remember that God rested on the seventh day, that does not mean that there was not an eighth day. As there was a new beginning in Noah, so in Christ, we have a new beginning in His resurrection on what is called the eighth day, or the first day of the week. The Lord Jesus went into the depth of the flood of mans sin. He took upon Himself the sin and darkness of the whole world. As He lay in the tomb, we have the cry of Isaiah in Isaiah 53:11, and 12.
He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities. (Isaiah 53:11)
Therefore will I divide him a portion with the great, and he shall divide the spoil with the strong; because he hath poured out his soul unto death: and he was numbered with the transgressors; and he bare the sin of many, and made intercession for the transgressors. (Isaiah 53:12)
  In this brief section our Lord’s soul is mentioned twice. First: it is the travail of his soul. Secondly: He poured out His soul unto death. This all took place in the hours of darkness within the tomb. The work of Christ on the cross was finished, but the work of eternity had just begun. Even now, the Lord Jesus is working in His justification of those who come to Him. This glorious realization of our redemption through His blood is shown forth in the burst of life and light of the Lord’s resurrection. He saw the travail of His soul, and He was, and is satisfied. In performing His servitude to God the Father, He is bring many to the eternal state, and rest in God’s eternity. The first day of the week became the eighth day, and in the Lord’s resurrection we have a new beginning for all mankind.
The Number Seven
  In the number seven (7) we have God’s completed work. In the number eight (8) we have God’s new beginning. All through Scripture we have this theme till it comes to its grand conclusion in the Book of the Revelation of Jesus Christ. The seventh day will end with the end of the millennial kingdom. This will be the last rebellion of man against God. This rebellion leads to the destruction of man, and his punishment at the great white throne. After the conclusion of this judgment, we have the ungodly cast into the lake of fire with Satan, the man of sin, and the false prophet.
  This seventh day is ended; finally, all of God’s work is finished with the sons of Adam. The eighth day begins with the creation of a new heaven and a new earth wherein righteousness will dwell among men in the Person of the most holy God, and His glory will be shed upon all.