3. In a right rectangular parallelepiped, the sum of all edges is $76 \mathrm{~cm}$, and the length of the diagonal is $13 \mathrm{~cm}$.

Calculate $(a+b-c) \cdot(a-b+c)+(a+b-c) \cdot(-a+b+c)+(a-b+c) \cdot(-a+b+c)$, where $a, b$ and c are the dimensions of the parallelepiped.
3. 

Let S be the sum of all edges, then $S=4(a+b+c)=76$, from which $a+b+c=19$

From $d=\sqrt{a^{2}+b^{2}+c^{2}}=13$ we get $a^{2}+b^{2}+c^{2}=169$

$E=(a+b+c)^{2}-2\left(a^{2}+b^{2}+c^{2}\right)$

Finalization $E=19^{2}-2 \cdot 169=361-338=23$