Here are the first six integers , which are sums of two cubes of positive integers

None of the numbers 9, 16, 28, 35, and 54 is a sum of two squares of integers,

while

Hence, the least integer which is a sum of two squares of integers and a sum

of two cubes of positive integers is 65.

Find few other positive integers which are sums of two squares and sums of two cubes of two relatively prime positive integers.

Generalize from your results.

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Few terms are :

72 = 2^3 + 4^3 = 6^2 + 6^2

370 = 3^3 + 4^3 = 3^2 + 19^2 = 9^2 + 17^2

468 = 5^3 + 7^3 = 12^2 + 18^2

Also,

128 = 4^3 + 4^3 = 8^2 + 8^2

250 = 5^3 + 5^3 = 5^2 + 15^2 = 9^2 +13^2

I am not sure, such terms are acceptable:

1024 = 8^3 + 8^3 = 0^2 + 32^2

If not acceptable, it needs to be specified in the definition itself.

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I asked to find few other positive integers which are sums of two squares and sums of two cubes of two relatively prime positive integers.

I could not consider the condition relatively prime in my above submission. As such, only one equation meets the required condition:

370 = 3^3 + 4^3 = 3^2 + 19^2