Let's say I am playing a 13th level character, 6 levels Bladesinger Wizard, 7 levels Eldritch Knight Fighter. I would have access to these abilities in question:
Beginning at 7th level, when you use your action to cast a cantrip, you can make one weapon attack as a bonus action.
Bladesinger's Extra Attack:
Starting at 6th level, you can attack twice, instead of once, whenever you take the Attack action on your turn. Moreover, you can cast one of your cantrips in place of one of those attacks.
With these rules in mind, is it viable to take the attack action, cast Booming Blade and make one weapon attack, and then because I cast a cantrip, also make another weapon attack with my bonus action?