Calculate: $$5^{2}+6^{2}+7^{2}+\cdots +15^{2}$$.  Kimmy\textquotesingle s answer to the question was $$1240$$, since $$\frac{15\times 16\times 31}{6}=1240$$.  Is Kimmy correct? If not, what should be the correct answer? 
Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas->1²+2²+3²+......+n²=1/6n(n+1)(n+2)