AMC 12 2022a 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?

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