list = Table[With[{e = i^k}, HoldForm[Sum[e, {i, 1, n}]]], {k, 5}];
Column[# == Factor[ReleaseHold[#]] & /@ list]

$$
begin{array}{l}
 sum _{i=1}^n i=frac{1}{2} n (n+1) \
 sum _{i=1}^n i^2=frac{1}{6} n (n+1) (2 n+1) \
 sum _{i=1}^n i^3=frac{1}{4} n^2 (n+1)^2 \
 sum _{i=1}^n i^4=frac{1}{30} n (n+1) (2 n+1) left(3 n^2+3 n-1right) \
 sum _{i=1}^n i^5=frac{1}{12} n^2 (n+1)^2 left(2 n^2+2 n-1right) \
end{array}
$$

$$
begin{array}{l}
 2sum _{i=1}^n i= n (n+1) \
 6sum _{i=1}^n i^2= n (n+1) (2 n+1) \
 4sum _{i=1}^n i^3= n^2 (n+1)^2 \
 30sum _{i=1}^n i^4= n (n+1) (2 n+1) left(3 n^2+3 n-1right) \
 12sum _{i=1}^n i^5= n^2 (n+1)^2 left(2 n^2+2 n-1right) \
end{array}
$$