We know that,

Total surface area of the cuboid = 2 (lh + bh + lb)

Total surface area of the cube = 6 (l)^{2}

Total surface area of cuboid (a) = [2{(60) (40) + (40) (50) + (50) (60)}] cm^{2}

= [2(2400 + 2000 + 3000)] cm^{2}

= (2 × 7400) cm^{2}

= 14800 cm^{2}

Total surface area of cube (b) = 6 (50 cm)^{2 }= 15000 cm^{2}

Thus, the cuboidal box (a) will require lesser amount of material.