\documentclass{article}


\usepackage{amsmath}

\begin{document}

$\sum_i a_i+\eta$\\
$\mathbf{\sum_{i=1}^n a_i+\eta}$\\
{\boldmath$\sum_{i=1}^n a_i+\eta$}\\
$\boldsymbol{\sum_{i=1}^n a_i+\eta}$\\
$\pmb{\sum_{i=1}^n a_i+\eta}$\\
$\boldsymbol{\pmb{\sum}_{i=1}^n a_i+\eta}$

\end{document}