It's also from Old French ("sucre"), Middle Latin ("succarum"), Persian ("shakar"), Sanskrit ("sharkara").
The Arabic word for sugar ("sukkar") was borrowed by Italian ('zucchero'), Spanish ('azucar') and Old High German ('zucura'; modern german: 'Zucker') because sugar was foreign in Europe until the Arabs began to cultivate it in Italy and Spain.
Since English is a Germanic language, "sugar" got its roots from the Old High German 'zucura', which was from the Arabic 'sukkar'.
Etymology is so interesting, isn't it? :]