If you're a high-elf fighter who has the Extra Attack feature, when you cast green-flame blade or booming blade, do you get to make your additional attacks?
If so, can you cast the spell again on those additional attacks?
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Related: What does upper-case-A-Attack action vs. lower-case-a-attack mean? – CTWind Nov 12 at 8:16
No, because Cast a Spell and Attack are different actions.
Green-flame blade says,
As part of the action used to cast this spell, you must make a melee attack...
When you cast this spell, you are taking the "Cast a Spell" action. As part of that action, you make a melee attack.
On the other hand, you must take the "Attack" action in order to use your extra attacks: (the Monk, PHB 79)
Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.
Because casting Green-Flame Blade is not the Attack action, you don't get to access your multiple attacks.
As a comparison, grappling explicitly states that you can grapple as one of your multiattack attacks (PHB 195):
If you’re able to make multiple attacks with the Attack action, this attack replaces one of them.
If Green-Flame Blade worked this way, it would say so as well.
No.
Casting either of those spells requires that you use your Action to Cast a Spell, even though the spell lets you make a melee attack with your weapon.
Extra Attack is only triggered when you take the Attack Action. There are several examples of Extra Attack in the PHB, so here's the one from Fighter in the PHB pg. 72, emphasis mine:
Extra Attack
Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.
Green Flame Blade and Booming Blade are both cantrips, which are covered under spellcasting rules. More importantly, both of them have a requirement of using 1 Action to be cast, and the melee attack is part of the spell.
