when timing a command execution time with sudo, `time` should be before `sudo` or after `sudo`?

time sudo command executes your shell's time builtin if it has one, whereas sudo time command always executes the time executable in the program search path ($PATH).

time sudo command includes the time taken by the sudo command, whereas sudo time command doesn't.

You should use sudo time command, because sudo's processing time is small but not always negligible, and its wall clock time may be a lot larger if the user needs to enter a password.