For the lost: The simple gospel: Christ died for our sins, according to the scriptures; He was buried, and that He rose again the third day, according to the scriptures. (1 Corinthians 15:3-4)
For the saved: The gospel explained in more detail: is the good news of the finished work (John 19:30) of the Lord Jesus Christ to save lost people from their sins (Matt 1:21). Sins are the manifold instances wherein man acts contrary to the Holy nature of Almighty God. Man breaks the revealed will of God in His 10 commandments (See Law of Moses - Exodus 20). This proves that man is both 1) a sinner by nature (Psalm 51:5); as a result of Adam's transgression (Romans 5:12), as well as 2) by his own practice (Romans 3:10-18, 5:12). All sinned in Adam (Romans 3:23), and all have sinned in practice (John 1:10). All are equally guilty before God. Sin is lawlessness, an attitude of independence from God and His will (1 John 3:4)
Adam fell from innocence in Eden, and his offspring are born spiritually dead (Ephesians 2:1). Man is therefore utterly incapable of doing anything to merit or obtain his own salvation (Romans 3:10-18) because he is ungodly and without strength (Romans 5:6). He must, and can be, saved through faith in Christ, apart from works (Romans 4:5), and that faith only comes by hearing the word of God (Romans 10:17). Thus the need is for the gospel to be proclaimed to him (Romans 10:14).
Moreover, because God is Holy (Isaiah 6:3), He shall and must punish sin. Since man can do nothing to fix or atone for his sin problem (Romans 3:20), the salvation of sinners is a gracious substitutionary work performed by the sacrifice of Christ (John 10:11) who by Himself purged our sins (Hebrews 1:3), perfected His people by His one offering (Hebrews 10:14), redeemed them by His blood (Hebrews 9:12), and declared the believer to be legally righteous, by virtue of Christ's obedience alone (Romans 5:19, 8:33). He who was dead in trespasses and sins (Ephesians 2:1), now has the eternal life of God (John 5:24).
The gospel is liberty to the captives (Isaiah 61:1) in that it proclaims the finished work of the Lord Jesus Christ on behalf of sinners as the sole means whereby men are eternally saved (Acts 4:12) and whereby they find rest (Matthew 11;28) and comfort (2 Corinthians (2 Corinthians 1;4). It is the declaration that Christ died for our sins, according to the scriptures; that He was buried, and that He rose again the third day, according to the scriptures. (1 Corinthians 15:3-4). The resurrection proves God's satisfaction in the work of His Son.
Believe on the Lord Jesus Christ and thou shalt be saved.
borrowed and heavily edited.