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The description of the darkness spell says:
If any of this spell’s area overlaps with an area of light created by a spell of 2nd level or lower, the spell that created the light is dispelled.
I take that to mean any existing spells. Does this also negate newly cast spells of 2nd level or lower? Would spells cast after the darkness spell work? If so, then the light cantrip with a light radius of 20 feet would completely counteract the 15 foot radius of darkness.
The cloud of Darkness would immediately snuff out the Light as soon as it was created. Note that the spell's text doesn't mention any restrictions or requirements involving which area effect, the Darkness or the Light, is created first. All that they need to do is overlap one another. If they overlap, even slightly, the Darkness instantly dispels the Light regardless of which was cast first.
The preferred spell to remove the entire cloud of Darkness is the 3rd-level evocation spell Daylight. However, theoretically, a 2nd-level Continual Flame spell cast with a 3rd-level spell slot could create light equivalent to a torch that would partially illuminate the Darkness but not permanently dispel it.
Entire description of Darkness (Player's Handbook, page 230):
Magical darkness spreads from a point you choose within range to fill a 15-foot-radius sphere for the duration. The darkness spreads around corners. A creature with darkvision can’t see through this darkness, and nonmagical light can’t illuminate it. If the point you choose is on an object you are holding or one that isn’t being worn or carried, the darkness emanates from the object and moves with it. Completely covering the source of the darkness with an opaque object, such as a bowl or a helm, blocks the darkness. If any of this spell’s area overlaps with an area of light created by a spell of 2nd level or lower, the spell that created the light is dispelled.
Emphasis mine. The spell's text implies that while nonmagical light cannot illuminate the magical darkness, magical light powerful enough not to immediately fizzle out can and will at least partially illuminate the darkened area.
