Exclude a digit using arithmetic sums

The total $1+\cdots+69=69(1+69)/2=2415$. The integers $30,31,\ldots,39$ sum to $10(30+39)/2=345$. The integers $3,13,23,\ldots,63$ sum to $7(3+63)/2=231$.

$33$ belongs to both excluded groups. Add it back once: $2415-345-231+33=1872$.