Sins of Ignorance or presumption.

When Paul spoke of the law, coming because of sin, I think he was referring to those sacrificial laws.

Before sin came, no sacrifice was needed, but when we knew sin, then that sin condemned us, because we would then need to remove that stain of sin, in our flesh, through the blood of animals. 

Those blood sacrifices though, never dwelt with the heart and mind. But because we have been salted with fire, and live as a living sacrifice, which HAS to be salted, our conscience is now clear, knowing now, that, those sins of ignorance have been paid.

Also, those ceremonial cleansing, the washing with water, mixed with the ashes of the heifer, is no longer needed, for those bodily functions.

It is those sins of presumption, after receiving the knowledge of the truth, thinking that we can now go and sin, because of His sacrifice, these we need to fear, and be ever mindful of, because there never has been, nor ever will be forgiveness for those premeditated, willful sins.

Num 15:29 Ye shall have one law for him that sinneth through ignorance, both for him that is born among the children of Israel, and for the stranger that sojourneth among them.
Num 15:30 But the soul that doeth ought presumptuously, whether he be born in the land, or a stranger, the same reproacheth the LORD; and that soul shall be cut off from among his people.
Num 15:31 Because he hath despised the word of the LORD, and hath broken his commandment, that soul shall utterly be cut off; his iniquity shall be upon him

Heb 10:26 For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins,