Do human beings naturally keep God's law (Romans 2:14-15)?

Can people keep the Torah (the law of God) without knowing the Torah? 

Is the Torah naturally written on our hearts so we can keep it?

"And the LORD smelled a sweet savour; and the LORD said in his heart, I will not again curse the ground any more for man's sake; for the imagination of man's heart is evil from his youth; neither will I again smite any more every thing living, as I have done." (Genesis 8:21) 

"Behold, I was shapen in iniquity; and in sin did my mother conceive me." (Psalm 51:5) 

1 Tim 1:13; Luke 12:47; Luke 23:34; John 9:39-41; James 4:17; Jonah 4:11; Matthew 12:41-42; 11:23-24; 1 Timothy 2:4; Romans 11:32

"Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience: Among whom also we all had our conversation in times past in the lusts of our flesh, fulfilling the desires of the flesh and of the mind; and were by nature the children of wrath, even as others." (Ephesians 2:2-3) 

Ephesians 4:17-20; Psalm 82:3-5; Psalm 147:19-20; Romans 10:18

"We who are Jews by nature, and not sinners of the Gentiles." (Gal 2:15)

Romans 1:18-32

"For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves: Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another." (Romans 2:14-15) 

"And shall not uncircumcision which is by nature, if it fulfil the law, judge thee, who by the letter and circumcision dost transgress the law?" (Romans 2:27) 

1 Corinthians 2:6-16