What class has the most damage output per round at level 6?

Question

I used to DM a group of players who liked to heavily optimize their characters (and the group as a whole) to take as little and deal as much damage as possible (seriously, these guys were crazy). It got to the point that I was routinely throwing encounters at them that would be considered "deadly" for a group of their level. Unfortunately, some of the members of that group moved away at around 6th level, so I never got to see how it carried on to later levels.

I recognize that this question is very broad, so to clarify and narrow it down a bit:

What is the most optimizable class from the Players Handbook for damage output per round in a single encounter, assuming the character:

• is fighting four Brown Bears
• has just finished a long rest
• has no magic items
• uses the standard ability array or point buy,
• has no buff effects from allies.

and to narrow it down further:

• use only RAW content from the Players Handbook

For the sake of clarity, let's define damage per round as the amount of damage a character can do averaged out between 5 consecutive rounds (assume the character doesn't die and the bears don’t die). Damage from Area of Effect spells hit all four bears.

Also, I'd like to state that I'm not looking for survivability here, so things like HP and AC are irrelevant.

Answer 1

Just Cast fireball A Lot

A sixth-level sorcerer has three third-level spell slots and six sorcery points. That sorcerer can get ten more sorcery points by converting their lower-level slots, and then convert ten sorcery points into two more third-level spell slots.  (We assume the sorcerer has a few rounds of downtime to do this before the battle.)

The sorcerer then can cast fireball five times, once per round, for an average damage of 28 before saves.

The sorcerer can apply Empowered Spell to each of their casts.  This lets them reroll up to four damage dice.  The average damage goes from 28 to 33.61 (according to my simulation).  Then, using Draconic Fire Bloodline, they can add their +4 CHA mod to the damage roll, for an average damage of 37.61.

A bear has a +0 DEX save, versus DC15, so it passes 30% of the time, which multiplies the damage by 0.85.  We multiply by four bears, and we get 127.8 damage per round.

If our race is tiefling, then we can also cast hellish rebuke once for 3d10*.85*.2=2.8 damage per round. The total is 130.6 damage per round.

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Can some other build do better?

I think sorcerer is the best class for this, simply because the sorcerer is the only class that can cast five fireballs at this level.  Multiclassing would worsen the build because it would lose the Elemental Affinity power which requires six levels of sorcerer.

I did not investigate other sorcerer options -- I just took the one that was visible on https://roll20.net/compendium/dnd5e/Sorcerer (Draconic with Fire), as it offered an additional +4 fireball damage and that seemed like a good deal.  It may be possible to do better using some other choice.

It's unfortunate that the sorcerer doesn't have a good damage-over-time spell to supplement all the fireballs, perhaps making use of their concentration or their bonus action or their reaction.  Unfortunately I didn't see anything promising on their spell list.