\(A=1\cdot2+2\cdot3+...+68\cdot69+69\cdot70\)
\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+69\cdot70\cdot\left(71-68\right)\)
\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+69\cdot70\cdot71-68\cdot69\cdot70\)
\(3A=69\cdot70\cdot71\Rightarrow A=\dfrac{69\cdot70\cdot71}{3}=114310\)