Given, edge of the cube = 21 cm

Now, radius the cone r = edge of cube/2

                                = 21/2 cm

and height of the cone h = edge of cube = 21 cm

Now, the volume of the cone is the largest right circular cone that can be cut out from a cube.

So, volume of the cone = πr² h/3

                                    = {(22/7)*(21/2)² * 21}/3

                                    = {22*21*21*7}/{7*2*2}

                                    = {22*21*21}/{2*2}

                                    = {11*21*21}/2

                                    = 4851/2

                                    = 2425.5 cm³

Again, volume of cube = (21)³ = 21 * 21 * 21 =  9261 cm³

So, the volume of remaining solid = volume of cube - volume of cone

                                                 = 9261 -  2425.5 = 6835.5 cm³

So, the volume of the remaining solid is 6835.5 cm³