Purpose Of Works

For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: not of works, lest any man should boast. (Ephesians 2:8-9 KJV)
So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by the works of the law, because by the works of the law no one will be justified. (Galatians 2:16b NIV)

If good works is not required for salvation, why do good? Why don't we continue sinning (Romans 6:1) since Jesus had already paid the penalty for our sins in full (Hebrews 10:14)?

Firstly, we do good works, not because we need them for our salvation, but we do it out of gratitude to our God who has so freely given everything to us (1 John 4:19, Ephesians 4:32, Colossians 3:12-13, Matthew 10:8). Our motivation is gratitude, not servitude.

Secondly, our works is an assurance of salvation to ourselves, showing that we are bearing fruits (Matthew 7:16, John 15:4).

Finally, our works is a witness to others of God's grace and salvation. As salt and light, God works through us to preserve and show His righteousness and to change the society. Our works glorify God.

God works through us. The only real work that God requires from us is to believe in Him (John 6:29).

Therefore, my beloved, as you have always obeyed, so now, not only as in my presence but much more in my absence, work out your own salvation with fear and trembling, for it is God who works in you, both to will and to work for his good pleasure. (Philippians 2:12-13 ESV)
And I am certain that God, who began the good work within you, will continue his work until it is finally finished on the day when Christ Jesus returns. (Philippians 1:6 NLT)