Python, 67 66 65 bytes
lambda a,b:sum(x*y*2for x in range(a,b+1) for y in range(x+1,b+1))
with @Dennis formulae and w/o recursion, yet another Python solution (as I cannot comment @leaky-nun solution (not enough reputation)
Python, 67 66 65 bytes
lambda a,b:sum(x*y*2for x in range(a,b+1) for y in range(x+1,b+1))
with @Dennis formulae and w/o recursion, yet another Python solution (as I cannot comment @leaky-nun solution (not enough reputation)