Compute $$1\cdot 2^2+2\cdot 3^2+3\cdot4^2+\cdots+19\cdot 20^2.$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute $$1\cdot 2^2+2\cdot 3^2+3\cdot4^2+\cdots+19\cdot 20^2.$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
41230
Compute $$1\cdot 2^2+2\cdot 3^2+3\cdot4^2+\cdots+19\cdot 20^2.$$
train