Shorter lines in tables can be obtained via \cline
which takes two integers separated by a dash in its argument, the first integer denoting the column where the line should start, the second integer denoting the column where the line should end.
However, I think you want to combine such a shorter line with a \hline
that spans over all columns. Sadly, \cline{2-7}\hline
would not work, but you can make use of the macro \hhline
provided by the hhline
package:
\documentclass{article}
\usepackage{siunitx}
\usepackage{hhline}
\begin{document}
\begin{tabular}{||c| c c c c c c||}
\cline{2-7}
\multicolumn{1}{c|}{} & W & Q & U & C & E & $\epsilon_0$\\
\hhline{-======}
SI & \si{\joule} & \si{\coulomb} & \si{\volt} & \si{\farad} & \si{\volt\per\meter} & \si{\coulomb\per\volt\per\meter}\\
\hline
base & & & & & & \\
\hline
\end{tabular}
\end{document}

If you want to remove the vertical line left of "W", you can go like this:
\documentclass{article}
\usepackage{siunitx}
\usepackage{hhline}
\begin{document}
\begin{tabular}{||c| c c c c c c||}
\cline{2-7}
\multicolumn{1}{c}{} & W & Q & U & C & E & $\epsilon_0$\\
\hhline{-======}
SI & \si{\joule} & \si{\coulomb} & \si{\volt} & \si{\farad} & \si{\volt\per\meter} & \si{\coulomb\per\volt\per\meter}\\
\hline
base & & & & & & \\
\hline
\end{tabular}
\end{document}

Maybe also have a look at the tabularray
package which provides more flexibility when it comes to cell borders (and provides for better spacing in my opinion):
\documentclass{article}
\usepackage{tabularray}
\usepackage{siunitx}
\begin{document}
\begin{tblr}{
colspec = { *{7}{c} },
hline{1} = {1}{2-Z}{},
hline{2} = {1}{2-Z}{},
hline{2-Z} = {2}{1-Z}{},
vline{1} = {1}{2-Z}{},
vline{1} = {2}{2-Z}{},
vline{2,Z} = {1}{1-Z}{},
vline{Z} = {2}{1-Z}{},
}
& W & Q & U & C & E & $\epsilon_0$ \\
SI & \si{\joule} & \si{\coulomb} & \si{\volt} & \si{\farad} & \si{\volt\per\meter} & \si{\coulomb\per\volt\per\meter} \\
base & & & & & & \\
\end{tblr}
\end{document}

\hlines
, use\cline{2-7}
(the argument takes two integers separated by a dash, the first integer denoting the column where the line should start, the second where the line should end.booktabs
package or rules which enablestabularray
package.