Packing 1×2×4 bricks in a cubical box

Given a cubical box C2n+1C2n+1 of side 2n+12n+1 and a supply of 1×2×4 bricks, it is proved that if n≥2n≥2, then (A1)one can pack n3+3n2+12 bricks for nn odd, and n3+3n22 bricks for nn even,(A2)the capacity of C2n+1C2n+1 is ≤12n(n+1)(2n+1), and if n≡1n≡1 or 2 (mod4)(mod4), this upper bound for the capacity can be reduced by 1.