Sum in each dimension
Mathematica, 32 20 bytes

#/.List-&gt;({##,+##}&amp;)&amp;


Example:

In[1]:= #/.List-&gt;({##,+##}&amp;)&amp;[{{1, 2, 3}, {4, 5, 6}}]

Out[1]= {{1, 2, 3, 6}, {4, 5, 6, 15}, {5, 7, 9, 21}}


Explanation:

The full form of {{1, 2, 3}, {4, 5, 6}} is List[List[1, 2, 3], List[4, 5, 6]]. Then replace all the Lists in the expression with the function ({##,+##}&amp;).