Do you celebrate the Mid-Autumn Festival? Do you remember the story ? How did this festival1?

    Long ago, our earth had ten suns. It was too2 for plants to grow, so everyone was poor and hungry.

    Hou Yi climbed to the3 mountain and shot down nine 4 He was a hero! As a reward, the God gave him a special medicine, and it can make him5forever. To keep the6safe, Hou Yi7it to his beautiful wife, Chang'e.

    One day Hou Yi was away. One of his followers, Peng Meng, tried to make Chang'e give him the medicine. Instead, Chang'e had to take it herself, and suddenly she8 up to the moon.

    When Hou Yi returned, he found Chang'e had gone and he missed her. Then he saw 9.It was very bright. A shadow on it looked just like 10.

    He set a table in the garden, with fruits and food for Chang'e.

    Now people still do the same at Mid-Autumn Festival.

如图，在平面直角坐标系 $xOy$ 中，已知椭圆 $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$ 的离心率为 $\frac{2}{3}$ ，C为椭圆上位于第一象限内的一点．

如图是某家族一种遗传病图解，请回答相关问题．（其中阴影部分的图为患病）

观察下列等式

1²=1= $\frac{1}{6}$ ×1×2×（2+1）

1²+2²= $\frac{1}{6}$ ×2×3×（4+1）

1²+2²+3²= $\frac{1}{6}$ ×3×4×（6+1）

1²+2²+3²+4²= $\frac{1}{6}$ ×4×5×（8+1）…

可以推测1²+2²+3²+…+n²=____．