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The relevant part of Hexblade's Curse states (XGtE p.55):

Starting at 1st level, you gain the ability to place a baleful curse on someone. As a bonus action, choose one creature you can see within 30 feet of you. The target is cursed for 1 minute. The curse ends early if the target dies, you die, or you are incapacitated. Until the curse ends, you gain the following benefits:

  • You gain a bonus to damage rolls against the cursed target. The bonus equals your proficiency bonus.
  • [...]

Typically when features add extra damage they clarify that the extra damage only applies to one damage roll, or the added damage just applies to the damage as a whole, like the various cleric subclasses' Potent Spellcasting:

Starting at 8th level, you add your wisdom modifier to the damage you deal with any cleric cantrip.

Or the Evocation Wizard's Empowered Evocation (PHB p.117):

…you can add your Intelligence modifier to one damage roll of any wizard evocation spell you cast.

Does this mean the wording of the Hexblade's Curse would apply to all of the dice rolled for the attack? If when the warlock gains Pact of the Blade at 3rd level, could they pick a great sword as there pact weapon, which deals 2d6 damage, and add their proficiency bonus twice to the damage?

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A "Damage Roll" can include multiple dice, but it still is a singular roll.

To quote the Player's Handbook about Damage Rolls (page 196), with added emphasis by me:

Each weapon, spell, and harmful monster ability specifies the damage it deals. You roll the damage die or dice, add any modifiers, and apply the damage to your target. Magic weapons, special abilities, and other factors can grant a bonus to damage.

Even if a greatsword has 2d6 for its damage, its Damage Roll would be: 2d6 + the relevant ability score modifier (normally Strength, but a Hexblade might use Charisma) + any additional bonuses (such as Hexblade's Curse, or Rage Damage).

The same logic applies to all features similar to Hexblade's Curse, including as a Cleric's Potent Spellcasting or a Wizard's Empowered Evocation.

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Hexblade's Curse, like other bonuses, applies once per hit

From DnDBeyond, after attacking a target...

You roll the damage die or dice, add any modifiers, and apply the damage to your target

(Emphasis mine)

The greatsword's weapon dice are 2d6, which are rolled, summed, and then Hexblade's Curse is added to that value along with any other modifiers

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