Question 11

What is the value of $$14^3 + 16^3 + 18^3 +....+ 30^3?$$

Solution

$$14^3 + 16^3 + 18^3 +....+ 30^3$$
=8($$7^3 + 8^3 + 9^3 +....+ 15^3$$)
Sum of n cubes =$$(n(n+1)/2)^2$$
for n=6 we have $$21^2$$=441
for n=15 we have $$120^2$$=14400
Difference=14400-441
=13959
Therefore 8*13959=111672

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What is the value of $$14^3 + 16^3 + 18^3 +....+ 30^3?$$

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