What scriptural arguments for the Trinity were used in the First Council of Nicea? What scriptural arguments for the Trinity were used in the First Council of Nicea?
We do not have any minutes or transcripts from the Council of Nicea. Bishop Theodoret of Cyrrhus, wrote his Ecclesiastical History  about 450 AD, though based on earlier sources. 

In Chapter 6 of Book 1 we may read that the Emperor Constantine, in his opening speech to the  Nicene Conference, urged the bishops to seek a solution (to their differences) in the divinely-inspired scriptures.  


  ‘For the gospels’ (continued he), ‘the  writings, and the oracles of the ancient prophets, clearly teach us what we ought to believe concerning the divine nature. Let, then, all contentious disputation be discarded; and let us seek in the divinely-inspired word the solution of the questions at issue.’ 


Chapter 7 quotes Athanasius, who was there, as saying the bishops collected together passages from the Scriptures relating to Christ. 

So it seems that the bishops looked to Scripture to ascertain the truth, or at least to argue their positions.   Still, the communique, to use a modern term, did not include  arguments  or scriptural references  justifying  the conclusion.

Athanasius did however describe  some of the  discussions at the Council as follows: 


  (some bishops made) the following declarations, which are in accordance with the holy Scriptures; namely, that the Son is by nature only-begotten of God, Word, Power, and sole Wisdom of the Father; that He is, as John said, 'the true God ,' and, as Paul has written, 'the brightness of the glory, and the express image of the person of the Father ,' 


and later


  collected from Scripture those passages which say of Christ that He is the glory, the fountain, the stream, and the express image of the person; and they quoted the following words: ' In your light we shall see light ;' and likewise, ' I and the Father are one. ' 


In Chapter 11 he quotes a letter from Eusebius who was also there 


  'We believe in the being and continual existence of each of these; that the Father is in truth the Father; the Son in truth the Son; the Holy Ghost in truth the Holy Ghost; as our Lord, when sending out His disciples to preach the Gospel, said, ' Go forth and teach all nations, baptizing them into the name of the Father, and of the Son, and of the Holy Ghost. '


The following appear to be some of the Scriptures referenced: (The phrases mentioned above are also listed below, but with the scriptures also listed.) 


"The Son is by nature only begotten of God"  John 1 18  and John 3 16



  
    And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
    
    For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
  



"Word, Power and sole Wisdom of the Father" John 1 1 Col 1 19 Col 2 9 and 1 Cor 1 24



  
    In the beginning was the Word, and the Word was with God, and the Word was God
    
    But unto them which are called, both Jews and Greeks, Christ the power of God, and the wisdom of God.
  



"the true God"  1 John 5 20



  
    And we know that the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, even in his Son Jesus Christ. This is the true God, and eternal life.
  



the brightness of the glory and the express image of the person of
the Father  Hebrews 1 3



  
    Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high;
  



"the glory"   John 1 14



  
    And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
  



"the fountain, in your light shall we see light" - links Psalm 36 9 with John 4 14 John 8 12 



  
    For with thee is the fountain of life: in thy light shall we see light.
    
    But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life.
    
    Then spake Jesus again unto them, saying, I am the light of the world: he that followeth me shall not walk in darkness, but shall have the light of life.
  



"I and the Father are One"  John 10 30



  
    I and my Father are one.    
  



"baptizing them in the Name of the Father, and of the Son, and of the
Holy Ghost;  Matthew 28 19Matthew 28 19


  
    Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: