[ textcolor{green}{sum}_{k=0}^n ]

newcommand*{opcolor}[2]{mathop{textcolor{#1}{#2}}}

documentclass{article}
usepackage{xcolor}
newcommand*{opcolor}[2]{mathop{textcolor{#1}{#2}}}
newcommand*{csum}[1]{opcolor{#1}sum}

begin{document}
[ mathop{textcolor{green}{sum}}_{k=0}^n ]

[ csum{green}_{k=0}^n ]

[ opcolor{green}{sum}_{k=0}^n ]
end{document}

documentclass{article}
usepackage{amsmath}
usepackage{xcolor}
begin{document}
[ mathop{textcolor{green}{sum}}_{k=0}^n ]
end{document}

documentclass{article}
usepackage{xcolor}
colorlet{mygreen}{green!80!black}% a littler darker

makeatletter
newcommand*{mathcolor}{}
% Catch an optional argument in #1
defmathcolor#1#{math@color{#1}}%
newcommand*{math@color}[3]{%
  % #1: empty or optional argument including brackets
  % #2: mandatory color argument
  % #3: stuff to be colored
  begingroupcolor#1{#2}#3endgroup
}
makeatother

begin{document}
[
  mathcolor{mygreen}{
    int_{mathcolor{black}{k=0}}^{mathcolor{black}{n}}
  }
  mathcolor{red}{=}
  mathcolor{mygreen}{
    intlimits_{mathcolor{black}{k=0}}^{mathcolor{black}{n}}
  }
]
end{document}