It was noted that Ethiopians (Nubians, Cushites, Africans) had different skin than the people of Israel (Jeremiah 13:23), but it was just a casual observation. There is nothing in the Bible suggesting that one race is superior to another.
Moses was married to a Cushite or Ethiopian woman. Moses' brother and sister, Aaron and Miriam, criticized that marriage, but God was angry with them for their criticism (Numbers 12:1-11).
The Hebrews were forbidden to marry Canaanites and other pagan peoples (Exodus 34:11-16; Deuteronomy 7:1-3). But the reason was because those people worshipped idols, not because of any racial differences.
Some English translations of the Bible use "race" to describe what we would think of today as national, ethnic or religious differences (Ezra 9:2, Wisdom 12:11, Zechariah 9:6). However, the Israelites, Canaanites, Philistines, etc. were all Middle Eastern peoples.
The apostle Paul encouraged Christians not to marry unbelievers (2 Corinthians 6:14), but here again, the reason was religious, not racial.
In His Parable of the Good Samaritan (Luke 10:25-37), Jesus told of a Samaritan man who was kind to a Jewish man even though they were enemies of different religions, nationalities and racial backgrounds. At the end, Jesus tells us, "Go and do likewise."
The apostle Paul taught the equality of all people without regard to racial/ethnic background, social status, or gender:
for in Christ Jesus you are all children of God through faith. As many of you as were baptized into Christ have clothed yourselves with Christ. There is no longer Jew or Greek, there is no longer slave or free, there is no longer male and female; for all of you are one in Christ Jesus. (NIV, Galatians 3:26-28)
Related Bible passages: Leviticus 19:18, Matthew 7:12, 22:34-40, Mark 12:28-31, Luke
6:31, 10:25-28, John 13:34-35, Romans 13:8-10, 15:1-2, James 2:8
Other references: Love Your Neighbor as Yourself,
What are the Greatest Commandment and the Parable of the Good Samaritan?,
What Does the Bible Say About Love?,
What Does the Bible Say About Interracial Marriage and Interracial Dating?
It has sometimes been said that the "mark of Cain" was a skin color difference (Genesis 4:15-16). But the Bible story does not give any hint that was the case. The mark is described as a sign or designation to indicate that Cain belonged to God and must not be harmed.
Some say the 3 races were the descendants of the three sons of Noah - Shem, Ham, and Japheth (Genesis 5:32). However, the genealogies given in the Bible (Genesis Chapter 10) do not support that conclusion. The peoples and nations mentioned there are mostly in the Middle East part of the world that was familiar to the Israelites.
Some say Noah’s curse of his grandson Canaan (Genesis 9:24-25) was a curse on a race. However, the descendants of Canaan, the Canaanites, were Middle Eastern people like the Israelites. They were considered "cursed" because they were enemies of the Israelites.
Some people see the origin of races in the story of the Tower of Babel (Genesis 11:1-9). However, the Bible says God confused peoples' languages, not that He changed their appearance.