Sum of three cubes

It is conjectured that all positive integers, not of the form $9\times k\pm 4$ can be written as a sum of 3 cubes, probably in infinitely many ways.

Some decompositions are hard to discover.

For instance, the smallest decomposition of 74 was only discovered in 2016:
$74=-{284650292555885}^3+{66229832190556}^3+{283450105697727}^3$

Decompositions for all integers up to 100 are known, except for 33 and 42.

Find all the decompositions of 1026 where the absolute value of each cube is $<{10}^5$.

Answer format: $Count,X,Y,Z\text{ where }X<Y<Z$ is the triple with the largest absolute values for X

You are given : 6,-14900,10849,12664 for 993 and a threshold of 20000.

$993=-{14900}^3+{10849}^3+{12664}^3$
$993=-{11450}^3-{4127}^3+{11626}^3$
$993=-{8339}^3+{6121}^3+{7051}^3$
$993=-{2528}^3+{673}^3+{2512}^3$
$993=-{1007}^3-{842}^3+{1174}^3$
$993=-2^3+1^3+{10}^3$

[My timing: 60 sec]