Step-by-step Solution:

To find the surface area of the resulting cuboid, we first need to find the side length of the original cubes and then use that to determine the dimensions of the new cuboid.

1. Find the side length of a single cube:
The volume of a cube is given by the formula \(V = a^3\), where \(a\) is the side length.
We are given that the volume is \(64 \text{ cm}^3\).
\[a^3 = 64\]\[a = \sqrt[3]{64} = 4 \text{ cm}\]
So, each cube has sides of length 4 cm.

2. Determine the dimensions of the resulting cuboid:
When two cubes with 4 cm sides are joined end to end, they form a cuboid.
The length of this new cuboid is the sum of the lengths of the two cubes.
Length \((l) = 4 \text{ cm} + 4 \text{ cm} = 8 \text{ cm}\).
The width and height of the cuboid remain the same as the side of a single cube.
Width \((w) = 4 \text{ cm}\).
Height \((h) = 4 \text{ cm}\).

3. Calculate the surface area of the cuboid:
The formula for the total surface area of a cuboid is \(A = 2(lw + wh + hl)\).
Substitute the dimensions \(l=8, w=4, h=4\) into the formula:
\[\begin{aligned} A &= 2((8)(4) + (4)(4) + (4)(8)) \\ &= 2(32 + 16 + 32) \\ &= 2(80) \\ &= 160 \text{ cm}^2 \end{aligned}\]
Result:
The surface area of the resulting cuboid is \(160 \text{ cm}^2\).