Tell us about yourself!
Folks who live in the US can use "Super glue" or "Krazy glue" or any cyanoacrylate for assembly. (Feviquick is a European product: I have never seen it here in the States."Also for US folks,your local Home Depot/Lowes is unlikely to stock 3mm but you will have equal results with 1/8" MDF and they will likely size it for you in the store if you know the max size of your laser cutter.Extra bonus for using "activator" during assembly to force the cyanoacrylate glue to dry faster! And if you want extra strength consider adding a back to your new cubbies or at least a "back stretcher" that's 6 or 8 cm high across the back, to provide extra strength against the shear forces collapsing your box diagonally.