At Central Middle School the $108$ students who take the AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of $15$ cookies, list these items: $\bullet$ $1\frac{1}{2}$ cups of flour $\bullet$ $2$ eggs $\bullet$ $3$ tablespoons butter $\bullet$ $\frac{3}{4}$ cups sugar $\bullet$ $1$ package of chocolate drops. They will make only full recipes, no partial recipes. Walter and Gretel must make enough pans of cookies to supply $216$ cookies. There are $8$ tablespoons in a stick of butter. How many sticks of butter will be needed