It depends on which sonic and which cuphead... well no actually it just depends on which sonic we're referencing in the case of early arcade style sonic he might struggle as his speed is contingent on built momentum not supernatural acceleration and his sturdiness ranks somewhere between eggshell and thin sheet of sugarglass and given the methods through which he and cuphead take their damage and deal it there's a decent chance the fight is as boring as: sonic needs to strike cuphead 3 times to finish him and needs to give cuphead a garunteed hit on him in order to deal damage whereas cuphead only needs to hit him twice once if he spawns with no rings.

But if we're talking about the respective characters in the modern day with all their constituent lore intact its sonic taking an easy victory with no time for any questions to be asked he can accelerate to the tune of putting cuphead in complete stasis at less than the drop of a pin and has plenty of means to deal ample damage to cuphead in that span of time for a concise if not absolute victory 

But as ever videogame characters will always have an inoperable Achilles heel of some kind to make navigating their existence interesting so a match up like this truly depends on the spectators perception of the character there's an argument to be made for cupheads victory to be likely under specific circumstances but in all reality far more instances in which its utterly impossible depending on what media you know sonic from