What is the Biblical basis the for Immutable Nature of God? Dei Filius sayeth this: 


  God cannot deny himself, nor can truth ever be in opposition to truth. The appearance of this kind of specious contradiction is chiefly due to the fact that either the dogmas of faith are not understood and explained in accordance with the mind of the Church, or unsound views are mistaken for the conclusions of reason.


and the Catechism quoteth it and sayeth this: 


  "because of the authority of God himself who reveals them, who can neither deceive nor be deceived"


Which is something I heardeth a priest say a few days ago in reference to 4th graders asking whether God can make a rock so big he can't lift it.  The Catholic answer is actually no, because God can't change His nature.

So, I'm going to go out on a limb here and assume that the Catholic Church's teaching on this is indeed based in Scripture.  But, since the references in the Catechism point to a Vatican I document, I'm not entirely sure which scripture (sounds like something St. Paul would say) or if it is just a teaching that is consistent with scripture. 

This is asked in regards to the documents (Dei Filius and CCC 156) and Catholic or Catholic leaning answers would be most appreciated.
Here are a few verses that support this:

Jesus Christ is the same yesterday, today, and forever.  Hebrews 13:8 NIV
Of old you laid the foundation of the earth, and the heavens are the
work of your hands.  They will perish, but you will remain; they will
all wear out like a garment. You will change them like a robe, and
they will pass away, but you are the same, and your years have no end.
Psalm 102:25-27 NIV
For I the LORD do not change; therefore you, O children of Jacob, are not consumed. Malachi 3:6
Every good gift and every perfect gift is from above, coming down from the Father of lights with whom there is no variation or shadow due to change.  James 1:17