Solution:

We can count the number of unexposed sides to find how many sides contribute to the surface area.

Three cubes have $1$ side unexposed, two cubes have $2$ sides unexposed, and one cube has $3$ sides unexposed.

This gives us a total of $$3 \cdot 1 + 2 \cdot 2 + 1 \cdot 3 = 10$$ unexposed sides, which gives us $$6 \cdot 6 - 10 = 36 - 10$$$$= 26$$ exposed sides.

Each exposed side contributes $1^2 = 1$ to the surface area, for a total surface area of $1 \cdot 26 = 26.$

Thus, C is the correct answer.