Before asking, I have checked Centered box, text inside it flushed right?, Questions about \fbox, and Any way to center text within a \parbox?.
Here I have tested various centering methods (my intention is to use \centering only) on \framebox and \makebox alike.
\framebox{This is a sentence of text.}\par
\makebox{This is a sentence of text.}\par
{\indent \centering\framebox{This is a sentence of text.}}\par
{\indent \centering\makebox{This is a sentence of text.}}\par
\framebox{\centering This is a sentence of text.}\par
\makebox{\centering This is a sentence of text.}\par
\framebox[5cm]{\centering This is a sentence of text.}\par
\makebox[5cm]{\centering This is a sentence of text.}\par
\framebox[\linewidth]{This is a sentence of text.}\par
\makebox[\linewidth]{This is a sentence of text.}\par
\framebox[5cm]{\centering This is a sentence of text.}\par
\makebox[5cm]{\centering This is a sentence of text.}\par
\framebox{\centering\parbox{5cm}{This is a sentence of text.}}\par
\makebox{\centering\parbox{5cm}{This is a sentence of text.}}\par
\parbox{5cm}{\centering\framebox{This is a sentence of text.}}\par
\parbox{5cm}{\centering\makebox{This is a sentence of text.}}\par
\begin{center}
\framebox{This is a sentence of text.}\par
\makebox{This is a sentence of text.}
\end{center}
The only standard LaTeX method (no packages) I can achieve is using the center environment (the last one). Is that so, and why?
An image is shown below. 
\parinside the group, not outside and you'll see something different. For example{...\centering...\par}. – Werner Aug 21 '13 at 14:40