Answer
$6050$
Work Step by Step
$\sum_{k=1}^{10} 2k^3=2\sum_{k=1}^{10} k^3$
The sum of the cubes of the first $n$ integers can be obtained by the following formula: $\frac{n^2(n+1)^2}{4}.$
Thus the sum:$\frac{10^2(10+1)^2}{4}=\frac{10^211^2}{4}=\frac{12100}{4}=3025$
Thus $2\sum_{k=1}^{10} k^3=2\cdot3025=6050$
