What is the value of 14^{3} + 16^{3} + 18^{3} | vedclass

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(D) The given series is $14^{3} + 16^{3} + 18^{3} + \ldots + 30^{3}$.This can be written as $\sum_{k=7}^{15} (2k)^{3} = 8 \sum_{k=7}^{15} k^{3}$.Using

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$111672$

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(D) The given series is $14^{3} + 16^{3} + 18^{3} + \ldots + 30^{3}$.This can be written as $\sum_{k=7}^{15} (2k)^{3} = 8 \sum_{k=7}^{15} k^{3}$.Using the formula for the sum of cubes,$\sum_{k=1}^{n} k^{3} = [\frac{n(n+1)}{2}]^{2}$.We need to calculate $8 [(\sum_{k=1}^{15} k^{3}) - (\sum_{k=1}^{6} k^{3})]$.$\sum_{k=1}^{15} k^{3} = [\frac{15 	imes 16}{2}]^{2} = (120)^{2} = 14400$.$\sum_{k=1}^{6} k^{3} = [\frac{6 	imes 7}{2}]^{2} = (21)^{2} = 441$.Sum $= 8 	imes (14400 - 441) = 8 	imes 13959 = 111672$.

What is the value of $14^{3} + 16^{3} + 18^{3} + \ldots + 30^{3}$?

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