Normally, you will perform this analysis using raster data. If the DTM contains enough detail (with the 2m² resolution) you would use this. Do you only have the DTM for 2001 and 2017 or do you also have multiple years? In case of only having the DTM for 2017 and 2001 (say you named those DTM2001 and DTM2017) you would calculate the difference (Minus—Help | ArcGIS Desktop ) DTM2017 - DTM2001. Each pixel in that case will indicate the increment in elevation (perhaps due to sediment as you mentioned). A value of +1 will indicate that in that pixel of 2x2m the volume increased 2*2*1= 4m³, a negative value will indicate a reduction of volume.
In case you have a polygon or a raster that indicates the area of interest, you can use the Zonal Statistics—Help | ArcGIS Desktop tool to get the total volume of change in that zone.
Since this will combine both the reduction and increment in volume, you may want to use a Con—Help | ArcGIS Desktop statement in the Raster Calculator to separate the positive and negative values (of the result of DTM2017 - DTM2001) first before doing the zonal statistics.