2022 AMC 12A Problem 14

What is the value of (\log 5)^3+(\log 20)^3+(\log 8)(\log 0.25) where \log denotes the base-ten logarithm?

\textbf{(A) } \frac{3}{2} \qquad \textbf{(B) } \frac{7}{4} \qquad \textbf{(C) } 2 \qquad \textbf{(D) } \frac{9}{4} \qquad \textbf{(E) } 3

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.