<image>To welcome the New Year, a certain district plans to design a triangular exhibition stand in the square. Gardeners are required to place an equal number of potted flowers along each side of the triangle to beautify the environment. Each small circle in the diagram represents one pot of flowers. For example, if 2 pots of flowers are placed on each side, a total of 3 pots are needed; if 3 pots are placed on each side, a total of 6 pots are needed; and so on, following this requirement,

(1) Fill in the table below according to the diagram:
\frac{}
(2) If n pots of flowers are to be placed on each side, then the total number of pots needed, s = ____;
(3) Please help the gardeners by determining whether 2010 pots of flowers can be used to meet the requirement. If so, calculate the number of pots that should be placed on each side; if not, explain the reason.