We propose a new search algorithm to solve the equation
x
3
+
y
3
+
z
3
=
n
x^3+y^3+z^3=n
for a fixed value of
n
>
0
n>0
. By parametrizing
|
x
|
=
|x|=
min
(
|
x
|
,
|
y
|
,
|
z
|
)
(|x|, |y|, |z|)
, this algorithm obtains
|
y
|
|y|
and
|
z
|
|z|
(if they exist) by solving a quadratic equation derived from divisors of
|
x
|
3
±
n
|x|^3 \pm n
. By using several efficient number-theoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. We performed a computer search for 51 values of
n
n
below 1000 (except
n
≡
±
4
(
mod
9
)
n\equiv \pm 4 (\operatorname {mod}9)
) for which no solution has previously been found. We found eight new integer solutions for
n
=
75
,
435
,
444
,
501
,
600
,
618
,
912
,
n=75, 435, 444, 501, 600, 618, 912,
and
969
969
in the range of
|
x
|
≤
2
⋅
10
7
|x| \le 2 \cdot 10^7
.