Psalm 14:1-3 The foolishness of living without God

14:4-6 The LORD is with the righteous

14:7 O that salvation would come out of Zion.

The Hebrew word translated "there is no" as in "there is no God" is used 4 times in verses 1-3. The first time man in saying in his heart that there is no God to call him to account. The other 3 times this Hebrew word is used in vs. 1-3 is God's assessment of man: there is none good. The word is used twice in vs. 1 and twice in vs. 3. 

Psalm 14 is virtually repeated in Psalm 53.  The small differences highlight a slightly different emphasis in these two psalms. Psalm 14  has unique phrases like the LORD is with the righteous generation  and the afflicted have made the LORD his refuge.  These unique phrases are emphasized in 14:5-6. In Psalm 53 verse 5 is unique as it speaks of scattering the bones of the wicked and it stresses God's judgment of the wicked.

Romans 3:10-12 quotes Psalm 14:1-3 and Psalm 53:1-3 and emphasizes that all have sinned and are in desperate need of His grace. 

Psalm 14 ends with longing that God would bring salvation out of Zion. This salvation is through His son Jesus Christ.