To express the prime factorization \( 23 \cdot 5^2 \cdot 11 \) as a whole number, we first need to calculate \( 5^2 \):
\[ 5^2 = 25 \]
Now we can substitute that value back into the expression:
\[ 23 \cdot 25 \cdot 11 \]
Next, we can multiply these together step by step. First, start with \( 23 \cdot 25 \):
\[ 23 \cdot 25 = 575 \]
Now, multiply that result by \( 11 \):
\[ 575 \cdot 11 = 6325 \]
Thus, the prime factorization \( 23 \cdot 5^2 \cdot 11 \) expressed as a whole number is:
\[ \boxed{6325} \]