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How is it possible for the infamous Sorlock multiclass to use 4 x Eldritch blasts in 1 round?

I get the extra damages as in the d6s and +mod damage from all the curses but I see formulas around like 4d10+4d6+64 (aasimar build), then 8d10+8d6+108.

How is this possible?

You don't need to be a Sorlock to create four eldritch blast beams in a round

Eldritch blast is a cantrip and all cantrips increase in damage as the PC levels. Eldritch blast, however, is pretty unique, in that rather than simply increasing in damage, at higher levels the caster instead fires additional beams, which all roll to hit and damage separately:

The spell creates more than one beam when you reach higher levels: two beams at 5th level, three beams at 11th level, and four beams at 17th level. You can direct the beams at the same target or at different ones. Make a separate attack roll for each beam.

So, any 17th level caster that knows eldritch blast will create four separate beams, whenever they cast eldritch blast (note: cantrips scale with total character level and not individual class level - so multi-classing won't delay cantrip upgrades).

So what does multi-classing to Sorcerer add to the mix?

Sorcerers have the feature Meta-magic, from which they can choose to use Quickened Spell:

When you cast a spell that has a casting time of 1 action, you can spend 2 sorcery points to change the casting time to 1 bonus action for this casting.

This means that a level 17 Sorlock (or a Sorcerer that knows Eldritch Blast by any other means), can spend 2 sorcery points in order to cast Eldritch Blast with both their action (as normal) and also their bonus action.

Four beams of Eldritch Blast for their action and another four beams for their bonus action equals eight beams in total. Blast off!

Side note: A Sorlock could actually get four beams in a round as early as level five using quickened spell (Sorcerer 3 / Warlock 2 if you want to benefit from agonizing blast too) - though they'd only have enough sorcery points be able to do that once a day without burning spell slots.

The formulas you're quoting are probably a level 20 Sorcerer/Hexblade Warlock, whose race is Protector Aasimar

First, to answer your specific question: any level 17+ character who can cast Eldrtich Blast would create 4 beams every time they cast it. And any Sorcerer Warlock with Eldrtich Blast and Quickened spell can cast Eldritch Blast twice in a turn (provided they have the Sorcery Points to do so). You can see explanations for both these facts below.

Now on to your larger question: you've seen a formula for:

4d10+4d6+64 (aasimar build), then 8d10+8d6+108.

And want to know "how is this possible?"

The specific formulas you've quoted require more than those two factors. There appear to be four factors coming together to create the equations you're describing:

1. Warlock's Eldritch Blast with Agonizing Blast invocation and Hex


2. Sorcerer's Quickened Spell


3. Protector Aasimar's Radiant Soul


4. Hexblade's Curse

All applied to a level 20 character. Here is how they come together

Eldritch Blast (& invocation & Hex)

The Eldritch Blast spell creates beams which do 1d10 + Charisma modifier damage per beam, provided you have the Agonizing Blast invocation. And the rules state (PHB, p. 237)

The spell creates more than one beam when you reach higher levels: two beams at 5th level, three beams at 11th level, and four beams at 17th level. You can direct the beams at the same target or at different ones. Make a separate attack roll for each beam.

Ever since an errata clarified matters, the rules on cantrips state the following (PHB, p. 164):

If a cantrip of yours increases in power at higher levels, the increase is based on your character level, not your level in a particular class.

So a level 20 character (even if they had only taken a couple of levels in Warlock) would create 4 beams every time they cast the spell Eldritch Blast. You could also cast the warlock spell Hex, which would allow you to add 1d6 damage per beam that hits. With a Charisma of 20 (practically a given by level 20), you would thus be dealing the following damage if all four hit.

• 4d10+4d6+(4*5)= 4d10+4d6+20

Sorcerer's Quickened Spell

The sorcerer's Quickened Spell metamagic permits the following (PHB, p. 102):

When you cast a spell that has a casting time of 1 action, you can spend 2 sorcery points to change the casting time to 1 bonus action for this casting.

A level 20 Sorcerer/Warlock (as long as they had at least 3 levels in Sorcerer, although most would have much more: most likely 17) could use their sorcery points to cast Eldritch Blast as a bonus action. They could also use their Action to cast Eldritch Blast in the same turn, since it is a cantrip with a casting time of 1 action (see PHB p.202 for rules on bonus action casting times to see why that's important). Thus, in one round you could cast the Eldritch Blast spell mentioned before twice. That would give you the following damage:

• 2*(4d10+4d6+20)= 8d10+8d6+40

Protector Aasimar's Radiant Soul

A Protector Aasimar (found in Volo's Guide to Monsters [VGtM]) can use their Radiant Soul feature to do the following for one minute once per long rest (VGtM, p. 105):

Starting at 3rd level, you can use your action to [transform]...
Your transformation lasts for 1 minute ... During it, ... once on each of your turns, you can deal extra radiant damage to one target when you deal damage to it with an attack or a spell. The extra radiant damage equals your level.

Thus, on one (and only one) of the beams each turn, a level 20 Protector Aasimar character (that had taken an action less than a minute ago to transform) could deal an extra 20 damage. So the total damage they could do with the previously mentioned tactics would be:

• (8d10+8d6+40)+20=8d10+8d6+60

Hexblade's Curse

A Hexblade Warlock (found in Xanathar's Guide to Everything [XGtE]) can use its Hexblade's Curse to gain several benefits. The most relevant is (XGTE, p. 55):

As a bonus action, choose one creature you can see within 30 feet of you. The target is cursed for one minute...

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

A level 20 character has a proficiency bonus of 6. Thus, they would add 6 damage to every beam of Eldritch Blast. Since the above strategy shoots 8 beams, they will do an extra 6*8=48 damage. So their total will be:

• (8d10+8d6+60)+48 = 8d10+8d6+108

So we've finally reached the total you mentioned above.

Also note that if you for some reason could only cast Eldritch Blast once in a turn with the remaining factors (Aasimar bonus, Hexblade bonus, Hex) in place, you would do the following damage

• 4d10 (four beams) + 4d6 (hex) + 4*5 (Agonizing Blast) + 4*6 (Hexblade's Curse) + 20 (Aasimar Radiant Soul)
  
  
  • = 4d10+4d6+64 (the first formula you mentioned).
  
  

You couldn't do this every round

Note that the preceding strategy would take one action and two bonus actions to set up (An action to activate Radiant Soul, a bonus action to cast Hex, and a bonus action to activate Hexblade's Curse). Thus, most characters couldn't be doing this much damage until at least the third round of combat. Also, the Aasimar's ability can only be used for one minute once a day, and the Hexblade's Curse can only be used once between short rests.

However, in the event all these sources of damage happen to come together, they could form a devastating total. And it is also worth keeping in mind, as Tiggerous pointed out, that a simple combination of Eldritch Blast and Quickened spell will allow you to cast Eldritch Blast twice in a turn. And higher level characters will create more beams per casting of Eldritch Blast. So even without these extra sources of damage, a Sorcerer/Warlock multiclass can often do damage many times in a single round.

One last thing...

It's possible that you weren't asking about attacking four times with Eldritch Blast, but rather casting Eldritch Blast four times in one turn? If so, this is also possible, but very hard to do.

I've addressed the specifics of how this could be done in my answer to another question.