If $a+b+c=6$ and $a b+b c+c a=10$, then the value of $a^3+b^3+c^3-3 a b c$ is:

36

We have,

If $a+b+c=6$ and $a b+b c+c a=10$, then the value of $a^3+b^3+c^3-3 a b c$

Note, if the number of equation is less then the number of variables then we can put extra variables according to our choice.

So, put c = 0

Then the equations reduced to = $a+b=6$ and ab=10

Now find $a^3+b^3$

$a^3+b^3$ = $6^3 - 3 × 10 × 6$

 $a^3+b^3+c^3-3 a b c$ or $a^3+b^3$ = 36