We know that,

Volume of cube = a³,

where a = side of cube

Now,

Side of first cube, a₁ = 3 cm

Side of second cube, a₂ = 4 cm

Side of third cube, a₃ = 5 cm

Now, Let the side of cube recast from melting these cubes is 'a'.

As the volume remains same,

Volume of recast cube = (volume of 1^st + 2^nd + 3^rd cube)

⇒ a³ = a₁³ + a₂³ + a₃³

⇒ a³ = (3)³ + (4)³ + (5)³

⇒ a³ = 27 + 64 + 125 = 216

⇒ a = 6 cm

So, side of cube so formed is 6 cm.