I am doing this work by hand, but it takes a lot of time and I make several calculation errors, so I was thinking to make Mathematica to calculate this for me, but I am stuck at the very beginning.

I am working with tensors like this:

$XXV\_{ijk} = \dfrac{1}{6}(X\_iX\_jV\_k+X\_iX\_kV\_j+X\_jX\_iV\_k+X\_kX\_jV\_i+X\_jX\_kV\_i+X\_kX\_iV\_j)$
$-\dfrac{1}{5}(\delta\_{ij}\, (X\cdot X) V\_k+\delta\_{ik} (X\cdot V) X\_j+\delta\_{jk} (X\cdot V) X\_i)$

where $X\_i$ and $V\_i$ are the components of the 3-vectors $\vec{X}$ and $\vec{V}$. I have to multiply these tensors, for example

$XXV \times XXV = \dfrac{2}{25}V^2+\dfrac{8}{25} (X\cdot V)^2$

I think I can obtain the first part with `Tuples` and `Total`(?) but I don't know how to obtain the part with the Kroeneker deltas; if I can write these tensors correctly I think I can multiply these tensors with `.` and `Transpose`.

As @yarchik has pointd out, I have to add that my tensors have unit length