The formation of the Christian canon was long underway by the time Constantine became the Roman emperor, and Constantine played very little role in the formation of the Christian canon, in either the decision to accept or reject the scriptural status of the Hebrew scriptures/Old Testament or in the decisions about which books to include in the New Testament.  Already in the late 1^st and early 2^nd centuries there is evidence that Christians were citing what came to be called the Old Testament as scripture, and even though Marcion (ca. 140) deliberately excluded the Jewish scriptures from his canon, his lead was not followed by the vast majority of Christian churches.  So this element of the canon was largely settled long before the time of Constantine.  With respect to the New Testament, again there is evidence already in the late 1^st and early 2^nd century of the citation of certain books in a “scriptural” way, although the term “scripture” is not yet typically applied to them.  Interestingly,  though, in 2 Peter (a New Testament text usually dated in the late 1^st or early 2^nd century) the author refers to the letters of Paul as authoritative and indicates that they are used in much the same way as the “other scriptures” (2 Pet. 3:16).  By the end of the 2^nd century many surviving texts had been written that testify to the emerging scriptural character of the books that would later form the canon of the New Testament.  There are numerous quotations of and allusions to the letters of Paul and the gospels of Matthew, Mark, Luke, and John in the letters of Clement and Ignatius, the Didache, the Shepherd of Hermas, the Epistle of Barnabas, the Letter of Polycarp to the Phillipians, Ptolemy’s Letter to Flora, and Justin Martyr’s Dialogue (see the Encyclopedia of Early Christianity, pp. 206-207).  And by the middle of the 2^nd century the term “scripture” was being applied to these specific Christian writings (see Justin Martyr’s First Apology 67).  By around 180 C.E. the terms “Old Testament” and “New Testament” were already being used to designate the Jewish and Christian scriptures (Irenaeus, Against Heresies, 4.28.1-2), and Irenaeus also specifically identifies the four gospels of Mark, Matthew, Luke, and John as the only ones that should be considered authoritative by Christians.  Brown’s claim that these gospels were only written or only came into vogue as a consequence of the decision in 325 C.E. to turn Jesus into a god (another falsehood, by the way) is simply ludicrous.  Eventually the Church moved from the acceptance of certain books as “scripture” toward a closed canon (in other words, the exclusion of any other books from “scriptural” status).  Again, though, this process was long underway by the time of Constantine, Constantine had almost nothing to do with it, and moreover it continued well after Constantine’s time.  Constantine did at one point request Eusebius of Caesarea to produce fifty copies of the Christian scriptures for use in the new capital city of Constantinople, but which scriptures to include in those copies was decided by Eusebius, and his decisions were simply accepted by the emperor.  There were many lists of books to include in the New Testament that were compiled before, during, and after the reign of Constantine.  Many of these lists (like the Muratorian canon, perhaps 180-200 C.E. and the lists of 3^rd century bishops like Origen and Tertullian) closely approximated the final version of the New Testament, at least in the consistent affirmation of the scriptural status of the four gospels (and no others), the letters of  Paul, and a few others (the Acts of the Apostles, 1 John).  Eusebius did compile a list at Constantine’s request, but he was apparently heavily influenced by these earlier lists, and certainly it was not the case that Eusebius’ decision was the final one.  The first list that corresponds to the list of twenty-seven books that is now accepted as comprising the New Testament canon is not compiled until 367 C.E.  (by Athanasius of Alexandria), which is of course long after the death of Constantine.  Moreover, even after this point there are many groups that did not accept some books on the list (esp. Hebrews, 2 Peter, Jude, and Revelation) and did accept others (esp. the letters of Clement and Barnabas and some Acts and Apocalypses).  So Constantine could not then have decided the issue.