What does the Bible say about the nature of our sin and God’s grace?

In the sermon, it is noted that Simon Peter fell at Jesus's feet, declaring, 'Depart from me, for I am a sinful man, O Lord' (Luke 5:8). This highlights the weight of our sinfulness before a holy God, as Romans 3:23 affirms that 'all have sinned and fall short of the glory of God.' However, through God's grace demonstrated in Christ, we have hope for redemption. Ephesians 2:4-5 declares, 'But God, who is rich in mercy, because of His great love with which He loved us, even when we were dead in trespasses, made us alive together with Christ.' Thus, while our sin is grave, God's mercy and grace are abundantly greater.