When you glue in the MDF, I suggest using Sikaflex 1A Polyurethane Premium Grade High Performance Elastomeric Sealant. It's a very strong adhesive but also maintains a slight flexibility, when cured, that has constrained layer damping properties.
Even Titebond I, II, and III have a little elasticity, even after curing. For a subwoofer cabinet, you do NOT want that. Stiffness is the operative word. Titebond makes a glue used by luthiers named Liquid Hide, and it's a synthetic version of the old cowhide glue furniture manufacture's use. It dries very hard, with no "give"---perfect for sub cabs, especially between the interior braces and the cabinet walls, and the edges of the six walls, where they are glued to each other. At those locations in a sub box, you do not want ANY lack of stiffness. Between the interior and exterior walls in a double wall box, constrained layer damping properties in the glue used may be a good idea. The slight movement between the two layers when vibrated by low frequencies won't effect the interior of the box, where you want the box to not flex at all, but the soft glues will perhaps damp the resonance of the exterior wall. Of course, if you build Danny's sand box you won't have any! Dead as a doornail (whatever THAT is), and quiet as a church mouse (ditto!). You don't hear the box, only the bass.
