Find a compact form for the sum $$\sum_{k=1}^n{{n}\choose{k}}k^{3}$$  I have been trying to solve this question for some time now. My guess is that I am supposed to write this in terms of something simpler (like a power of a simple sum) but I just can't come up with anything. I would appreciate it if you could give me a hint before providing the full answer so I can think about it on my own.
I am trying to solve the following question which is Ex3 from Arthur Engel, Problem Solving strategies. Here is the question: $\sum_{k=1}^n k^3 {n \choose k}$ and asks to find the sum. I am sincerely having a hard time trying to figure out how to solve it and get $n^2 (n+3)(2)^{n-3}$. I would really appreciate if someone could show the step-by-step process. Thank you!
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