Find the value of 13
3
+(−8)
3
+(−5)
3
.

We can use the algebraic identity:
If a+b+c=0, then a
3
+b
3
+c
3
=3abc.

Let a=13, b=−8, and c=−5.

a+b+c=13+(−8)+(−5)=13−13=0
Therefore:

13
3
+(−8)
3
+(−5)
3
=3×13×(−8)×(−5)
=3×13×40
=39×40=1560