The \@part macro is the one that must be changed here if numbered \parts are under consideration.
The \partname\nobreakspace\thepart construct is used in \@part in the book.cls (and in report as well)
A patch with \xpatchcmd can be applied in order to strip the \partname\nobreakspace content and use \textcolor{partnumbercolour}{\thepart} instead only.
Redefinition of \partname may break other features, I don't recommend it here.
Since the user class is loading book only, \AtBeginDocument{...} might be necessary to make the change effective.
\documentclass{book}
\usepackage{xcolor}
\usepackage{xpatch}
\colorlet{partnumbercolour}{blue}
\makeatletter
\AtBeginDocument{
\xpatchcmd{\@part}{\partname\nobreakspace\thepart}{\textcolor{partnumbercolour}{\thepart}}{}{}
}
\makeatother
\begin{document}
\part{Foo}
\part{Foobar}
\end{document}

\part(actually\@part) depends on the underlying class. You should provide at least a compilable document – Sep 05 '17 at 21:55