The problem requires finding the number of buckets, each holding 6.25 liters, needed to fill a tank with a volume of 1 cubic meter ($m^3$).
First, convert the tank's volume from cubic meters to liters, as the bucket capacity is given in liters.
Divide the total volume of the tank (in liters) by the capacity of one bucket (in liters) to find the number of buckets required.
Calculation: $ \frac{1000}{6.25} = \frac{1000}{\frac{625}{100}} = 1000 \times \frac{100}{625} = \frac{100000}{625} = 160 $
Thus, 160 such buckets are needed to fill the 1 cubic meter tank.