The surface area \( S \) of a rectangular prism can be calculated using the formula:
\[ S = 2lw + 2lh + 2wh \]
where \( l \), \( w \), and \( h \) are the lengths of the edges of the prism.
In this case, since all edges are equal (the prism is a cube), each edge length is \( 15.1 \) cm. Therefore, we have:
- \( l = 15.1 , \text{cm} \)
- \( w = 15.1 , \text{cm} \)
- \( h = 15.1 , \text{cm} \)
Now plug in the values:
\[ S = 2(15.1)(15.1) + 2(15.1)(15.1) + 2(15.1)(15.1) \]
This simplifies to:
\[ S = 6 \times (15.1 \times 15.1) \]
Calculating \( 15.1 \times 15.1 \):
\[ 15.1 \times 15.1 = 228.01 , \text{cm}^2 \]
Now multiply by 6:
\[ S = 6 \times 228.01 = 1368.06 , \text{cm}^2 \]
Thus, the surface area of the rectangular prism is:
\[ \boxed{1368.06 , \text{cm}^2} \]