Full weeks in Tikz Calendar

In a very simply way with tikZ this can be done using the dates key and if (<test date>) [<style>] path of the calendar command. Both are well documented in the PGFmanual. There can be more clever solutions. With this solution for example with the following code:

documentclass[border=3mm]{standalone}
usepackage{tikz}
usetikzlibrary{calendar}
newcommand{calOfTheMonth}[4]{%
calendar [dates=2021-0#1-01+-#2 to 2021-0#1-last+#3,week list,month yshift=0pt]
if (between=2021-0#1-01+-#2 and 2021-0#1-01+-1) [gray]
if (between=2021-0#1-last+1 and 2021-0#1-last+#3) [gray];
node[above=3ex,anchor=west] {#4};}
begin{document}
%Explanation of the calOfTheMonth macro
% calOfTheMonth{n. of the month}{days to add before}{days to add after}{name of the month}
tikz
matrix{
calOfTheMonth{1}{4}{0}{January}
calOfTheMonth{2}{0}{0}{February}
calOfTheMonth{3}{0}{4}{March}
calOfTheMonth{4}{3}{2}{April}
calOfTheMonth{5}{5}{6}{May}
calOfTheMonth{6}{1}{4}{June}
calOfTheMonth{7}{3}{1}{July}
calOfTheMonth{8}{6}{5}{August}
calOfTheMonth{9}{2}{3}{September}
calOfTheMonth{10}{4}{0}{October}
calOfTheMonth{11}{0}{5}{November}
calOfTheMonth{12}{2}{2}{December}
};
end{document}