Tabularx environment

Here are two solutions. The first uses a tabularx environment, with all six columns using a centered version of the X column type. The second uses a tabular* environment, with all six columns using the c column type. Both solutions occupy the full width of the textblock.

Since \multicolumn{1}{l}{} does nothing at all, you might as well omit those instructions.

\documentclass{article}
\usepackage{multirow,tabularx,booktabs}
\newcommand{\mr}[1]{\multirow{2}{*}{#1}} % handy shortcut macro
% centered version of X column type:
\newcolumntype{C}{>{\centering\arraybackslash}X} 

\usepackage[skip=0.333\baselineskip]{caption} % optional

\begin{document}
\begin{table}
%%\centering  % <-- redundant
\caption{tabularx}
\begin{tabularx}{\textwidth}{@{} *{6}{C} @{}}
\toprule
1         & 2      & 3      & 4      & 5      & 6 \\
\midrule
\mr{Pepe} & \mr{a} & \mr{b} & \mr{c} & \mr{d} & e \\
          &        &        &        &        & f \\
\midrule
  &  &  &  &  &  \\ % no need for "\multicolumn{1}{l}{}" stuff
\bottomrule
\end{tabularx}

\vspace{1cm} %
\setlength\tabcolsep{0pt}
\caption{tabular*}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} *{6}{c} }
\toprule
1         & 2      & 3      & 4      & 5      & 6 \\
\midrule
\mr{Pepe} & \mr{a} & \mr{b} & \mr{c} & \mr{d} & e \\
          &        &        &        &        & f \\
\midrule
  &  &  &  &  &  \\ % no need for "\multicolumn{1}{l}{}" stuff
\bottomrule
\end{tabular*}
\end{table}
\end{document} 

As @daleif mentioned you forgot to add the second bracket with your columns' specification {cccccc}. Probably there is a reason why you want to use the tabularx environment from the tabularx package.

The pack­age de­fines an en­vi­ron­ment tab­u­larx, an ex­ten­sion of tab­u­lar which has an ad­di­tional col­umn des­ig­na­tor, X, which cre­ates a para­graph-like col­umn whose width au­to­mat­i­cally ex­pands so that the de­clared width of the en­vi­ron­ment is filled. (Two X columns to­gether share out the avail­able space be­tween them, and so on.)

I guess you want to adapt the width of the first column as shown in the following example.

I give you the according code as a MWE:

\documentclass{article}
\usepackage{tabularx}
\usepackage{multirow}
% The [following] pack­age en­hances the qual­ity of ta­bles [...]
\usepackage{booktabs}
% Macro to simplify the code
\newcommand{\mr}[1]{\multirow{2}{*}{#1}}

\begin{document}
\begin{table}
\caption{My caption}
\centering
\begin{tabularx}{.5\textwidth}{Xccccc}
\toprule
1         & 2      & 3      & 4      & 5      & 6 \\
\midrule
\mr{Pepe} & \mr{a} & \mr{b} & \mr{c} & \mr{d} & e \\
          &        &        &        &        & f \\
\midrule
  &  &  &  &  &  \\
\bottomrule
\end{tabularx}
\end{table}
\end{document}

Supplement

Additionally, keep in mind that there is a package called tabu, which is more powerful than tabularx.

You do not need multicolumns in every cell, nor \multirow{2}{*}{...}, nor tabularx or tabular* to extend the text width, nor empty rows. Here you have enough with m columns (of array package) and, of course, with booktabs: :)

\documentclass{article}
\usepackage{graphicx,array,booktabs}
\begin{document}
\begin{table}
\caption{My caption}
\newcolumntype{C}{>{\centering\arraybackslash}m{\dimexpr\linewidth/6-2\tabcolsep}}
\begin{tabular}{CCCCCC}\toprule
1  & 2 & 3 & 4 & 5 & 6 \\\midrule
Pepe & a & b & c  & d &e\par f\\\bottomrule
\end{tabular}
\end{table}
\end{document}

By the way, I would not use columns of more two-three em here. Widening the table as much as possible instead of a small centered table does not make it more beautiful, but ugly scattered.