What is the largest integer $n$ such that  $$(1 + 2 + 3 + \cdots+ n)^2 < 1^3 + 2^3 + \cdots+ 7^3?$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the largest integer $n$ such that  $$(1 + 2 + 3 + \cdots+ n)^2 < 1^3 + 2^3 + \cdots+ 7^3?$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
6
What is the largest integer $n$ such that  $$(1 + 2 + 3 + \cdots+ n)^2 < 1^3 + 2^3 + \cdots+ 7^3?$$
train