A rectangular board of $8$ columns has squares numbered beginning in the upper left corner and moving left to right so row one is numbered $1$ through $8$, row two is $9$ through $16$, and so on. A student shades square $1$, then skips one square and shades square $3$, skips two squares and shades square $6$, skips $3$ squares and shades square $10$, and continues in this way until there is at least one shaded square in each column. What is the number of the shaded square that first achieves this result?

Let's think step by step and output the final answer within \boxed{}.
user