How to remove Section, SubSection titles?

You can define a \fakesection that does all the things the regular \section does except print the actual heading:

\newcommand{\fakesection}[1]{%
  \par\refstepcounter{section}% Increase section counter
  \sectionmark{#1}% Add section mark (header)
  \addcontentsline{toc}{section}{\protect\numberline{\thesection}#1}% Add section to ToC
  % Add more content here, if needed.
}

A similar macro for \fakesubsection would be

\newcommand{\fakesubsection}[1]{%
  \par\refstepcounter{subsection}% Increase subsection counter
  \subsectionmark{#1}% Add subsection mark (header)
  \addcontentsline{toc}{subsection}{\protect\numberline{\thesubsection}#1}% Add subsection to ToC
  % Add more content here, if needed.
}

The uses would be \fakesection{some section} and \fakesubsection{some subsection}.

I can't see any application for this setting: without any visual clue in the text, a table of contents containing inexistent titles doesn't make sense.

However, one can do it with titlesec, ensuring that the references will be correct, both in the table of contents and with the \label-\ref mechanism.

\documentclass{book}

\usepackage{lipsum}

\usepackage{titlesec}

\makeatletter
\titleformat{\section}[runin]{}{}{0pt}{\@gobble}
\titleformat{\subsection}[runin]{}{}{0pt}{\@gobble}
\makeatother
\titlespacing{\section}{\parindent}{0pt}{0pt}
\titlespacing{\subsection}{\parindent}{0pt}{0pt}

\begin{document}
\tableofcontents

\chapter{Chapter 1}

\section{Section 1}

\subsection{Subsection 1}

Here is lovely paragraph. And notice there is a ``subsection title'' 
right above me. How do I get rid of that title thingy?

\subsection{Subsection 2}

More stuff:
\[
1+2+3+\cdots+\infty=-\frac{1}{12}
\]
\lipsum[1-10]

\section{Section 2}
\lipsum[1-10]

\end{document}

Table of contents page

First chapter page