I defined a few different blocks with different colors. Now, the problem is that when I want to use \itemize, still the color of bullets are the same as predefined colors as blue by Beamer. Thanks.
\documentclass{beamer}
\setbeamertemplate{caption}[numbered]% <-- added, for other option see beamer manual, page 124
\usepackage{subcaption}
\setbeamersize{text margin left=8mm,text margin right=8mm}
\titlegraphic{\includegraphics[width=3cm]{NTHU_Logo_Gray.pdf}}
\usepackage{amsthm,amssymb,amsmath,dsfont} % in new xepersian package,
\usepackage{textpos}
\usepackage[utf8]{inputenc}
\DeclareUnicodeCharacter{FFFD}{\colorbox{Blue}{\color{white}?}}
\usepackage{array}
\newenvironment<>{examplefirst}[1]{%
\centering
\setbeamercolor{itemize item}{fg=green}
\setbeamercolor{block title}{fg=white,bg=green!40!black}%
\begin{block}#2{#1}}{\end{block}}
\newenvironment<>{examplefirst2}[1]{%
\centering
\setbeamercolor{itemize item}{fg=red}
\setbeamercolor{block title}{fg=white,bg=red!90!black}%
\begin{block}#2{#1}}{\end{block}}
\usetheme{Frankfurt}
\usecolortheme{whale}
\begin{document}
\begin{frame}
\onslide<+->{\begin{examplefirst}{case 1}
\begin{itemize}
\item 1
\item 2
\end{itemize}
\end{examplefirst}}
\onslide<+->{\begin{examplefirst2}{case 2}
\begin{itemize}
\item 1
\item 2
\end{itemize}
\end{examplefirst2}}
\end{frame}
\end{document}
structure
colour, though this is rather a guess in the absence of a proper example.