Cube expressible as a sum of consecutive cubes in two distinct ways

 
 
The sum of   k   consecutive cubes beginning with   m^3   is :

m^3 \; + \; (m+1)^3 \; + \; (m+2)^3 \; + \; \dotsb \; + \; (m+k-1)^3
= \; (k/4) \; (k + 2 \, m - 1) \, (k^2 + 2 \, k \, m - k + 2 \, m^2 - 2 \, m)

 
 

The cube   2856^3   is expressible as a sum of consecutive cubes in two distinct ways:

2856^3 \; = \; 213^3 \; + \; 214^3 \; + \; 215^3 \; + \; \dotsb \; + \; 555^3
2856^3 \; = \; 273^3 \; + \; 274^3 \; + \; 275^3 \; + \; \dotsb \; + \; 560^3

 
 
Can you find another example?
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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