The volume of a cube with sides of length L is given by L^3.

We have the volume of the cube as 343.

L^3 = 343

=> L^3 = 7^3

=> L = 7

The surface area of a cube of length L is 6*L^2. As L = 7, the surface area is 6*7^2 = 6*49 = 294 square units.

**The required surface area is 294 square units.**

Given that the volume of the cube is 343

Let x be the length of the side of the cube.

Then we know that V = x^3 = 343

==> x = 7

Now let us calculate the surface are.

The surface area of the cube = area of one surface * 6

\==> The area of one of the surface = x^2 = 7^2 = 49

==> Then the surface area = 49* 6 = 294.

**Then, the surface area of the cube is 294 square units.**