Here’s a really quick answer. There was a Syrian sun god called Elagabal (Lord of the sun), and one of the emperors, Heliogabalis (which is a Latin version of the name) was a priest of that god. When he became emperor, he took the religion with him to Rome, where Elagabal was worshiped under the name “Sol Invictus” (the conquering son). Heliogabalis was crazy, decadent, and was killed and overthrown, and the worship of Sol Invictus faded into the background.
50 years later, the emperor Aurelian took the throne (in 270). Aurelian , who beleved in Mithraicism, revived the worship of Sol Invictus, associated Sol Invictus with Mithras, and made the worship of Sol Invictus part of the official state cult.
Remember that in ancient, prechristian Rome, religion took one of two forms…there was an individual’s personal religion, which the state, in general didn’t care about, and then there was the official state religion, which was funded and regulated by the State. So, by making Sol Invictus part of the offical pantheon, and associating him with Mithras, what Aurelian was doing was giving the worship of Mithras governmental support.
So, from Aurelian to Contstantine, the Cult of Sol Invictus and the mysteries of Mithras coexisted, both as independent entites, but with a good deal of overlap.
Aldebaran has a point, though IMHO his perspective does not do justice to the Constantine-Christianity connection.
Constantius’s first wife, (H)Elen, was a committed Christian; she was Constantine’s mother, and presumably taught him her faith in his early childhood, prior to Constantius divorcing her. To what extent that teaching remained a part of Constantine’s psychology and personal beliefs is something one can only infer from his actions and utterances.
The worship of the sun, as Helios/Sol Invictus and associated with Apollo and Mithras in a syncretic belief structure, was indeed popular among the Army in the late Third and early Fourth Centuries. It was “the soldier’s faith.” Christianity was a minority belief in the Army, though it was growing in popularity throughout the Empire.
Constantine’s actions were no doubt a combination of personal belief and political expediency, as are most religiously-influenced actions of people with political power throughout history.
The “deathbed baptism” of Constantine is not a factor in deciding his belief – since it was common understanding at the time that baptism wiped away sin, and that while sin after baptism could be forgiven, it required a long and demeaning public penance to do so. Ergo, most believers put off baptism until late in their lives, to get the maximum cleansing effect from it. Several early Church writers remark on this as a common practice (which they usually deplored).
To what extent he was a sincere believer in Christianity at any given time in his life is debatable – but there is little doubt that he did adopt it as his faith.
BTW, the Edict of Toleration is, according to my reading, something forced by the Constantine faction on Licinius, not the latter’s idea at all.